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 "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract"
-"2419363","Conference: Workshop on Computational and Applied Enumerative Geometry","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/15/2024","05/14/2024","Luis Garcia Puente","CO","Colorado College","Standard Grant","James Matthew Douglass","04/30/2025","$22,500.00","Taylor Brysiewicz, Nickolas Hein","lgarciapuente@coloradocollege.edu","14 E CACHE LA POUDRE ST","COLORADO SPRINGS","CO","809033243","7193896318","MPS","126400","7556","$0.00","The ""Workshop on Computational and Applied Enumerative Geometry"" will be held June 3 to June 7, 2024 at the Fields Institute in Toronto, ON, Canada. Enumerative geometry is the study of a particular class of mathematical problems, called enumerative problems, which are fundamental to STEM fields including mathematics, particle physics, robotics, and computer vision. The main goal of this workshop is to unite experts working on problems related to enumerative geometry to increase dialogue between theory and application. There will be several talks on state-of-the-art research in computational and applied enumerative geometry, software demonstrations, and time to discuss open problems. The exchange of ideas will inform experts as they continue devising computational investigations of enumerative problems going forward. The grant supports the participation of fifteen US-based participants in the workshops. <br/><br/>Classically, an enumerative problem asks how many geometric objects have a prescribed position with respect to other fixed geometric objects. Famous examples include the problems of (a) 2 lines meeting four lines, (b) 27 lines on a cubic surface, and (c) 3264 conics tangent to five conics in the plane. A modern definition of an enumerative problem is a system of polynomial equations in variables and parameters with finitely many solutions given fixed generic parameters.  Counting solutions to such a problem is the tip of the iceberg.  Beyond enumeration lie questions of symmetries, solvability, real behavior, and computation.  Techniques from a broad range of disciplines lend themselves to the creation of algorithms and software designed to answer these questions. ""Computational Enumerative Geometry"" refers to this approach of using computers to solve, experiment with, and prove theorems about, enumerative problems. The workshop website is  http://www.fields.utoronto.ca/activities/23-24/enumerative-geometry.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
+"2419363","Conference: Workshop on Computational and Applied Enumerative Geometry","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/15/2024","05/14/2024","Luis Garcia Puente","CO","Colorado College","Standard Grant","James Matthew Douglass","04/30/2025","$22,500.00","Nickolas Hein, Taylor Brysiewicz","lgarciapuente@coloradocollege.edu","14 E CACHE LA POUDRE ST","COLORADO SPRINGS","CO","809033243","7193896318","MPS","126400","7556","$0.00","The ""Workshop on Computational and Applied Enumerative Geometry"" will be held June 3 to June 7, 2024 at the Fields Institute in Toronto, ON, Canada. Enumerative geometry is the study of a particular class of mathematical problems, called enumerative problems, which are fundamental to STEM fields including mathematics, particle physics, robotics, and computer vision. The main goal of this workshop is to unite experts working on problems related to enumerative geometry to increase dialogue between theory and application. There will be several talks on state-of-the-art research in computational and applied enumerative geometry, software demonstrations, and time to discuss open problems. The exchange of ideas will inform experts as they continue devising computational investigations of enumerative problems going forward. The grant supports the participation of fifteen US-based participants in the workshops. <br/><br/>Classically, an enumerative problem asks how many geometric objects have a prescribed position with respect to other fixed geometric objects. Famous examples include the problems of (a) 2 lines meeting four lines, (b) 27 lines on a cubic surface, and (c) 3264 conics tangent to five conics in the plane. A modern definition of an enumerative problem is a system of polynomial equations in variables and parameters with finitely many solutions given fixed generic parameters.  Counting solutions to such a problem is the tip of the iceberg.  Beyond enumeration lie questions of symmetries, solvability, real behavior, and computation.  Techniques from a broad range of disciplines lend themselves to the creation of algorithms and software designed to answer these questions. ""Computational Enumerative Geometry"" refers to this approach of using computers to solve, experiment with, and prove theorems about, enumerative problems. The workshop website is  http://www.fields.utoronto.ca/activities/23-24/enumerative-geometry.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
+"2409099","Conference: 2024-2026 Graduate Student Conference in Geometry, Topology, and Algebra","DMS","ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","05/15/2024","05/15/2024","Matthew Stover","PA","Temple University","Standard Grant","Swatee Naik","04/30/2027","$90,000.00","David Futer, Jaclyn Lang","mstover@temple.edu","1805 N BROAD ST","PHILADELPHIA","PA","191226104","2157077547","MPS","126400, 126700","7556","$0.00","This award supports the next three events in the Annual Graduate Student Conference series in Algebra, Geometry, and Topology (GTA Philadelphia). The next conference will be held on May 31-June 2, 2024 at Temple University. The conference will bring together over 80 graduate students at all levels and from a variety of backgrounds and universities, along with four distinguished plenary speakers that work at the interface of algebra, geometry, and topology. Supplementing lectures by faculty and students, the conference features a professional development panel focused on career building and social responsibility. The conference provides a rare opportunity for a large number of early career mathematicians with similar research interests to come together and develop mathematical relationships. In addition, it strongly supports interactions between graduate students from different schools, different backgrounds, and different research areas.<br/><br/>The large majority of lectures will be given by graduate students, supplying them with opportunities to practice presenting their research ideas and interests to fellow students. The conference strives to include a wide range of topics and a broad diversity of speakers. In addition, talks by distinguished plenary speakers will provide insights into how different parts of algebra, geometry, and topology are connected, open research questions of interest, and recent techniques used in groundbreaking work in these fields. For further information, see https://math.temple.edu/events/conferences/gscagt/.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
+"2401461","Zeros of L-functions and Arithmetic","DMS","ALGEBRA,NUMBER THEORY,AND COM, EPSCoR Co-Funding","07/01/2024","05/15/2024","Micah Milinovich","MS","University of Mississippi","Standard Grant","Andrew Pollington","06/30/2027","$252,360.00","","mbmilino@olemiss.edu","113 FALKNER","UNIVERSITY","MS","386779704","6629157482","MPS","126400, 915000","9150","$0.00","This award concerns research in number theory which is a very active area of mathematics, and the theory of L-functions, which were first introduced into the subject by Dirichlet in the 19-th century to study the distribution of prime numbers, has played a central role in its modern development. The tools used to study L-functions draw from many fields including analysis, algebra, algebraic geometry, automorphic forms, representation theory, probability and random matrices, and mathematical physics. Many of the projects in this proposal concern the connection between problems in number theory and the distribution of zeros of L-functions. This connection is central to two of the seven Millennium Prize Problems, the Riemann hypothesis and the Birch and Swinnerton-Dyer conjecture. This award aims to use tools from the theory of L-functions to make new progress on some classical problems in number theory as well as establish new connections between the theory of L-functions to fields such as additive combinatorics. The PI will continue training and mentoring graduate students on topics related to this research, and this project will provide research training opportunities for them.<br/> <br/>One goal of this project aims to use tools from Fourier analysis, along with input from zeros of L-functions, to study classical problems in number theory such as bounding the least quadratic non-residue modulo a prime, the least prime in an arithmetic progression, and the maximum size of modulus and argument of an L-functions on the critical line. Each of these problems requires using explicit formulae (connecting zeros of L-functions to the primes) to create a novel Fourier optimization framework and then to solve the resulting problem in analysis. This project also aims to study a number of problems concerning the L-functions associated to classical holomorphic modular forms, including studying simultaneous non-vanishing of L-functions at the central point, using sieve methods to studying non-vanishing of central values of L-functions in certain sparse (but arithmetically interesting) families, and to study the proportion of the non-trivial zeros of a modular form L-function that are simple. Using known partial progress toward the Birch and Swinnerton-Dyer conjecture, some of these proposed problems have applications to studying algebraic ranks of elliptic curves. Another goal of this project is to use tools from the theory of L-functions in a novel way to investigate problems in additive combinatorics such as studying sums of dilates in certain arithmetically interesting groups.<br/><br/><br/>This project is jointly funded by Algebra and Number Theory program, and the Established Program to Stimulate Competitive Research (EPSCoR).<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2339274","CAREER: New directions in the study of zeros and moments of L-functions","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","02/12/2024","Alexandra Florea","CA","University of California-Irvine","Continuing Grant","Tim Hodges","06/30/2029","$87,350.00","","alexandra.m.florea@gmail.com","160 ALDRICH HALL","IRVINE","CA","926970001","9498247295","MPS","126400","1045","$0.00","This project focuses on questions in analytic number theory, and concerns properties of the Riemann zeta-function and of more general L-functions. L-functions are functions on the complex plane that often encode interesting information about arithmetic objects, such as prime numbers, class numbers, or ranks of elliptic curves. For example, the Riemann zeta-function (which is one example of an L-function) is closely connected to the question of counting the number of primes less than a large number. Understanding the analytic properties of L-functions, such as the location of their zeros or their rate of growth, often provides insight into arithmetic questions of interest. The main goal of the project is to advance the knowledge of the properties of some families of L-functions and to obtain arithmetic applications. The educational component of the project involves groups of students at different stages, ranging from high school students to beginning researchers. Among the educational activities, the PI will organize a summer school in analytic number theory focusing on young mathematicians, and will run a yearly summer camp at UCI for talented high school students.<br/><br/>At a more technical level, the project will investigate zeros of L-functions by studying their ratios and moments. While positive moments of L?functions are relatively well-understood, much less is known about negative moments and ratios, which have applications to many difficult questions in the field. The planned research will use insights from random matrix theory, geometry, sieve theory and analysis. The main goals fall under two themes. The first theme is developing a general framework to study negative moments of L-functions, formulating full conjectures and proving partial results about negative moments. The second theme involves proving new non-vanishing results about L-functions at special points. Values of L-functions at special points often carry important arithmetic information; the PI plans to show that wide classes of L-functions do not vanish at the central point (i.e., the center of the critical strip, where all the non-trivial zeros are conjectured to be), as well as to study correlations between the values of different L-functions.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2347095","Collaborative Research: Conference: Texas-Oklahoma Representations and Automorphic forms (TORA)","DMS","ALGEBRA,NUMBER THEORY,AND COM","01/01/2024","12/19/2023","Kimball Martin","OK","University of Oklahoma Norman Campus","Standard Grant","Andrew Pollington","12/31/2026","$20,000.00","Ameya Pitale","kmartin@math.ou.edu","660 PARRINGTON OVAL RM 301","NORMAN","OK","730193003","4053254757","MPS","126400","7556, 9150","$0.00","This award supports the TORA mathematics conference series. This series consists of annual meetings hosted by the University of North Texas, Oklahoma State University, and the University of Oklahoma on a rotating basis. This award provides support for three weekend conferences, one at the University of North Texas in Spring 2024 (TORA XIII), one at Oklahoma State University in Spring 2025 (TORA XIV), and another at the University of Oklahoma in Spring 2026 (TORA XV). Each conference will feature three prominent guest speakers from outside the Texas-Oklahoma region, in addition to other participants including students, post-doctoral researchers, and junior faculty. Regional graduate students and researchers will also give talks describing their work. These conferences will facilitate collaborations and interactions among the students and researchers in the region who work in the areas of Automorphic Forms, Representation Theory, and Number Theory.<br/><br/>Over the last century, the theories of automorphic forms and representations have grown enormously. Important applications impact various fields of research, ranging from number theory, coding theory, algebraic geometry, and topology to Kac-Moody algebras and quantum field theory. The interplay of automorphic forms and representation theory has been especially fruitful, and many surprising and deep results have emerged. The TORA conference series will emphasize the interplay between automorphic forms and representations, both in the classical and adelic languages, and related topics like analytic number theory and harmonic analysis.<br/><br/><br/><br/>The conference Texas-Oklahoma Representations and Automorphic forms XIII will take place on April 12-14, 2024, at the University of North Texas. Additional information can be found on the conference website: https://www.math.unt.edu/~richter/TORA/TORA13.html<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2401184","Representation Theory and Geometry in Monoidal Categories","DMS","ALGEBRA,NUMBER THEORY,AND COM","09/01/2024","04/04/2024","Daniel Nakano","GA","University of Georgia Research Foundation Inc","Continuing Grant","Tim Hodges","08/31/2027","$88,519.00","","nakano@math.uga.edu","310 E CAMPUS RD RM 409","ATHENS","GA","306021589","7065425939","MPS","126400","","$0.00","The Principal Investigator (PI) will investigate the representation theory of various algebraic objects. A representation of an abstract algebraic object is a realization of the object via matrices of numbers. Often times, it is advantageous to view the entire collection of representations of an algebraic object as a structure known as a tensor category. Tensor categories consist of objects with additive and multiplicative operations like the integers or square matrices. Using the multiplicative operation, one can introduce the spectrum of the tensor category which is a geometric object (like a cone, sphere or torus). The PI will utilize the important connections between the algebraic and geometric properties of tensor categories to make advances in representation theory. The PI will continue to involve undergraduate and graduate students in these projects. He will continue to be an active member of the mathematical community by serving on national committees for the American Mathematical Society (AMS), and as an editor of a major mathematical journal.<br/><br/>The PI will develop new methods to study monoidal triangular geometry. Several central problems will utilize the construction of homological primes in the general monoidal setting and the introduction of a representation theory for MTCs. This representation theory promises to yield new information about the Balmer spectrum of the MTC. In particular, the general MTC theory will be applied to study representations of Lie superalgebras. The PI will also explore new ideas to study representations of classical simple Lie superalgebras. This involves systematically studying various versions of Category O and the rational representations for the associated quasi-reductive supergroups. One of the main ideas entails the use of the detecting and BBW parabolic subgroups/subalgebras. Furthermore, the PI will study the orbit structure of the nilpotent cone and will construct resolutions of singularities for the orbit closures. The PI will study important questions involving representations of reductive algebraic groups. Key questions will focus on the understanding the structures of induced representations, and whether these modules admit p-filtrations. These questions are interrelated with the 30-year-old problem of realizing projective modules for the Frobenius kernels via tilting modules for the reductive algebraic group, and the structure of extensions between simple modules for the first Frobenius kernel.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
@@ -26,7 +28,6 @@
 "2349623","Invariant Rings, Frobenius, and Differential Operators","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","04/03/2024","Anurag Singh","UT","University of Utah","Continuing Grant","Tim Hodges","05/31/2027","$82,544.00","","singh@math.utah.edu","201 PRESIDENTS CIR","SALT LAKE CITY","UT","841129049","8015816903","MPS","126400","","$0.00","This project will investigate several questions in commutative algebra, a field that studies solution sets of polynomial equations. The research will yield concrete information about the properties of solution sets of such equations. Polynomial equations arise in a wide number of applications; one fruitful approach to their study is via studying polynomial functions on their solution sets, that form what is known as a commutative ring. This offers an enormous amount of flexibility in studying solutions sets in various settings, and indeed commutative algebra continues to develop a fascinating interaction with several fields, becoming an increasingly valuable tool in science and engineering. A key component of this project is the training of graduate students in topics connected with the research program.<br/><br/><br/>The focus of the research is on questions related to local cohomology, differential operators, and the property of having finite Frobenius representation type. Local cohomology often provides the best answers to fundamental questions such as the least number of polynomial equations needed to define a solution set; this will be investigated for solution sets related to certain rings of invariants. The differential operators that one encounters in calculus make sense in good generality on solution sets of polynomial equations and are proving to be an increasingly fruitful object of study. Similarly, finite Frobenius representation type, first introduced for the study of differential operators, is proving to be a very powerful property with several applications.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2337942","CAREER: Arithmetic Dynamical Systems on Projective Varieties","DMS","ALGEBRA,NUMBER THEORY,AND COM","09/01/2024","01/22/2024","Nicole Looper","IL","University of Illinois at Chicago","Continuing Grant","Tim Hodges","08/31/2029","$36,742.00","","nrlooper@uic.edu","809 S MARSHFIELD AVE M/C 551","CHICAGO","IL","606124305","3129962862","MPS","126400","1045","$0.00","This project centers on problems in a recent new area of mathematics called arithmetic dynamics. This subject synthesizes problems and techniques from the previously disparate areas of number theory and dynamical systems. Motivations for further study of this subject include the power of dynamical techniques in approaching problems in arithmetic geometry and the richness of dynamics as a source of compelling problems in arithmetic. The funding for this project will support the training of graduate students and early career researchers in arithmetic dynamics through activities such as courses and workshops, as well as collaboration between the PI and researchers in adjacent fields.<br/><br/>The project?s first area of focus is the setting of abelian varieties, where the PI plans to tackle various conjectures surrounding the fields of definition and S-integrality of points of small canonical height. One important component of this study is the development of quantitative lower bounds on average values of generalized Arakelov-Green?s functions, which extend prior results in the dimension one case. The PI intends to develop such results for arbitrary polarized dynamical systems, opening an avenue for a wide variety of arithmetic applications. A second area of focus concerns the relationship between Arakelov invariants on curves over number fields and one-dimensional function fields, and arithmetic on their Jacobian varieties. Here the project aims to relate the self-intersection of Zhang?s admissible relative dualizing sheaf to the arithmetic of small points on Jacobians, as well as to other salient Arakelov invariants such as the delta invariant. The third goal is to study canonical heights of subvarieties, especially in the case of divisors. A main focus here is the relationship between various measurements of the complexity of the dynamical system and the heights of certain subvarieties. The final component of the project aims to relate the aforementioned generalized Arakelov-Green?s functions to<br/>pluripotential theory, both complex and non-archimedean.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2346615","Conference: Zassenhaus Groups and Friends Conference 2024","DMS","ALGEBRA,NUMBER THEORY,AND COM","01/01/2024","11/08/2023","Yong Yang","TX","Texas State University - San Marcos","Standard Grant","Tim Hodges","12/31/2024","$18,000.00","Thomas Keller","yy10@txstate.edu","601 UNIVERSITY DR","SAN MARCOS","TX","786664684","5122452314","MPS","126400","7556","$0.00","This award supports participation in the 2024 Zassenhaus Groups and Friends Conference which will be held at Texas State University in San Marcos, TX. It will take place on the campus of the university from noon of Friday, May 31, 2024, to the early afternoon on Sunday, June 2, 2024. It is expected that about 40 researchers will attend the conference, many of whom will give a talk. <br/><br/>The Zassenhaus Groups and Friends Conference, formerly known as Zassenhaus Group Theory Conference, is a series of yearly conferences that has served the mathematical community since its inception in the 1960s. The speakers are expected to come from all over the country and will cover a broad spectrum of topics related to the study of groups, such as representations of solvable groups, representations of simple groups, character theory, classes of groups, groups and combinatorics, recognizing simple groups from group invariants, p-groups, and fusion systems.<br/><br/>The conference will provide group theory researchers in the US a forum to disseminate their own research as well as to learn about new and significant results in the area. The conference will provide a particularly inviting environment to young mathematicians and will inspire future cooperation and collaborations among the participants. It is expected that it will have great impacts on the group theory research community. The organizers will make great effort to attract a demographically diverse group of participants including women and racial and ethnic minorities. More information can be found at the conference website, https://zassenhausgroupsandfriends.wp.txstate.edu/<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
-"2402637","Conference: Connecticut Summer School in Number Theory 2024","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/15/2024","04/03/2024","Alvaro Lozano-Robledo","CT","University of Connecticut","Standard Grant","Adriana Salerno","03/31/2025","$29,967.00","Keith Conrad, Jennifer Balakrishnan, Christelle Vincent","alvaro.lozano-robledo@uconn.edu","438 WHITNEY RD EXTENSION UNIT 11","STORRS","CT","062699018","8604863622","MPS","126400","7556","$0.00","The Connecticut Summer School in Number Theory (CTNT 2024) is a conference for advanced undergraduate and beginning graduate students, to be followed by a research conference, taking place at at the University of Connecticut, Storrs campus, from June 10 through June 16, 2024. Even though the northeast of the United States is a hotspot for number theory research, there is no instructional school in number theory that occurs in this region. Undergraduate and beginning graduate students who are interested in number theory may only have had an elementary number theory course during college. The CTNT summer school will achieve several outcomes: expose undergraduate and beginning graduate students to accessible topics that are fundamental to contemporary number theory; provide an environment where students interested in number theory can meet each other and network with students, postdocs, and faculty from institutions where number theory is a strong research area; train a diverse group of students on topics of current importance in number theory; allow advanced undergraduates and beginning graduate students to attend a research conference in number theory; videotape the lectures and post them online at a dedicated website to reach as wide of an audience as possible later: https://ctnt-summer.math.uconn.edu/<br/> <br/>CTNT 2024 will consist of a 4.5-day summer school followed by a 2-day conference. The summer school will have six mini-courses on topics important to contemporary number theory that are not available in a typical college curriculum, such as elliptic curves, reciprocity, adeles and ideles, and class field theory.  The courses will be complemented with course projects, daily invited talks, evening problem sessions, and discussion panels about aspects of graduate school (both for those already in graduate school and those thinking of applying). The conference will consist of several sessions with research talks in number theory, arithmetic geometry, and related topics, and it will be an opportunity for young researchers to present their work.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2400089","Higher Representation Theory and Subfactors","DMS","ALGEBRA,NUMBER THEORY,AND COM, ANALYSIS PROGRAM, EPSCoR Co-Funding","07/01/2024","04/10/2024","Cain Edie-Michell","NH","University of New Hampshire","Standard Grant","Tim Hodges","06/30/2027","$172,165.00","","cain.edie-michell@unh.edu","51 COLLEGE RD","DURHAM","NH","038242620","6038622172","MPS","126400, 128100, 915000","9150","$0.00","This project will involve research into quantum symmetry. The notion of symmetry is fundamental in classical physics. A famed result of Emmy Noether shows that for each symmetry of the laws of nature, there is a resulting conserved physical quantity. For example, the time invariance of the laws of physics results in the law of conservation of energy. In the setting of quantum physics, the more general notion of quantum symmetries is required to understand the behavior of the system. This project concerns the study of how quantum symmetries act on certain systems, with the end goal being to fully understand and classify these actions. We refer to these actions of quantum symmetries as `higher representation theory?. Particular emphasis will be placed on the examples which are relevant to topological quantum computation. This project will involve research opportunities for undergraduate students at the University of New Hampshire.<br/><br/>More technically, the notion of quantum symmetry is characterized mathematically by a tensor category, and the actions of quantum symmetries are characterized by module categories over these tensor categories. This project will study fundamental problems on the construction and classification of module categories. The following research problems will be addressed: 1) construct and classify the module categories over the tensor categories coming from the Wess-Zumino-Witten conformal field theories, 2) construct new continuous families of tensor categories which interpolate between the categories coming from conformal field theories, 3) use Jones?s graph planar algebra techniques to study Izumi?s near-group tensor categories, and 4) investigate the higher categorical objects related to the module categories in 1).<br/><br/>This project is jointly funded by the Algebra and Number Theory program and the Established Program to Stimulate Competitive Research (EPSCoR).<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2402553","Torsors under Reductive Groups and Dualities for Hitchin Systems","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/04/2024","Roman Fedorov","PA","University of Pittsburgh","Standard Grant","Tim Hodges","06/30/2027","$250,000.00","","fedorov@pitt.edu","4200 FIFTH AVENUE","PITTSBURGH","PA","152600001","4126247400","MPS","126400","","$0.00","The study of torsors (also known as principal bundles) began in the early 20th century by physicists as a formalism to describe electromagnetism. Later, this was extended to encompass strong and weak interactions, so that torsors became a basis for the so-called Standard Model - a physical theory describing all fundamental forces except for gravitation. The standard model predicted the existence of various particles, the last of which, called the Higgs boson, was found in a Large Hadron Collider experiment in 2012. In 1950's Fields medalist Jean-Pierre Serre recognized the importance of torsors in algebraic geometry. In his 1958 seminal paper he gave the first modern definition of a torsor and formulated a certain deep conjecture. The first part of this project is aimed at proving this conjecture, which is among the oldest unsolved foundational questions in mathematics. The second part of the project is related to the so-called Higgs bundles, which can be thought of as mathematical incarnations of the Higgs bosons. More precisely, the PI proposes to prove a certain duality for the spaces parameterizing Higgs bundles. This duality is a vast generalization of the fact that the Maxwell equations describing electromagnetic fields are symmetric with respect to interchanging electrical and magnetic fields. The duality is a part of the famous Langlands program unifying number theory, algebraic geometry, harmonic analysis, and mathematical physics. This award will support continuing research in these areas. Advising students and giving talks at conferences will also be part of the proposed activity.<br/><br/>In more detail, a conjecture of Grothendieck and Serre predicts that a torsor under a reductive group scheme over a regular scheme is trivial locally in the Zariski topology if it is rationally trivial. This conjecture was settled by Ivan Panin and the PI in the equal characteristic case. The conjecture is still far from resolution in the mixed characteristic case, though there are important results in this direction. The PI proposes to resolve the conjecture in the unramified case; that is, for regular local rings whose fibers over the ring of integers are regular. A more ambitious goal is to prove the purity conjecture for torsors, which is, in a sense, the next step after the Grothendieck?Serre conjecture. The second project is devoted to Langlands duality for Hitchin systems, predicting that moduli stacks of Higgs bundles for Langlands dual groups are derived equivalent. This conjecture may be viewed as the classical limit of the geometric Langlands duality. By analogy with the usual global categorical Langlands duality, the PI formulates a local version of the conjecture and the basic compatibility between the local and the global conjecture. The PI will attempt to give a proof of the local conjecture based on the geometric Satake equivalence for Hodge modules constructed by the PI.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2408333","Conference: GAeL XXXI (Geometrie Algebrique en Liberte)","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/01/2024","03/15/2024","Jose Rodriguez","WI","University of Wisconsin-Madison","Standard Grant","Tim Hodges","03/31/2025","$16,255.00","","jrodriguez43@wisc.edu","21 N PARK ST STE 6301","MADISON","WI","537151218","6082623822","MPS","126400","7556","$0.00","This award  funds participation of  junior US mathematicians in the 31st edition of Gael (Géométrie Algébrique en Liberté) from June 17-21, 2024 at Turin, Italy, held jointly by Politecnico di Torino and Università di Torino. Géométrie Algébrique en Liberté is a series of annual meetings organized for and by junior researchers in algebraic geometry with a long tradition, drawing in 70-90 participants each year. There are both casual and structured career opportunities for junior mathematicians to interact with speakers and other attendees. <br/><br/>GAeL XXXI will bring together leading experts on a range of topics within Algebraic Geometry, providing an excellent opportunity for junior mathematicians to learn about major new developments. There will be three senior speakers giving mini-courses covering cutting edge results from a wide variety of topics so that GAeL appeals to all PhD students and junior postdocs in algebraic geometry. The rest of the talks are chosen from among the junior participants, often providing the first opportunity for many of these individuals to speak in front of an international audience. More information about GAeL XXXI may be found on the event website: https://sites.google.com/view/gaelxxxi<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
@@ -34,10 +35,11 @@
 "2348833","Studies in Categorical Algebra","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/01/2024","04/03/2024","Chelsea Walton","TX","William Marsh Rice University","Continuing Grant","Tim Hodges","04/30/2027","$119,965.00","","notlaw@rice.edu","6100 MAIN ST","Houston","TX","770051827","7133484820","MPS","126400","","$0.00","Algebraic structures have been employed for nearly two centuries to understand the behavior, particularly the symmetry, of various entities in nature. Now with the current technology of category theory (i.e., the study of objects and how they are transported), classical algebraic structures can be upgraded to provide information on natural phenomena that was not previously understood. This yields significant consequences in quantum physics. The work sponsored by this grant lies in the framework of monoidal categories, which are categories that come equipped with a way of combining objects and combining maps between objects. Several projects are earmarked for partial work by undergraduate and graduate students. Moreover, the PI will make significant progress on completing a three-volume, user-friendly textbook series on quantum algebra. The PI is also an active mentor for numerous members of underrepresented groups, particularly for those in groups to which the PI belongs (women, African-Americans, and first generation college students).<br/><br/>The first research theme of the projects sponsored by this grant is on algebras in monoidal categories. The PI will extend classical properties of algebras over a field to the monoidal context, and will also study properties that only have significant meaning in the categorical setting. In addition, the PI will examine other algebraic structures (e.g., Frobenius algebras) in monoidal categories, especially those tied to Topological Quantum Field Theories (TQFTs). Another theme of the PI's sponsored research work is on representations of certain monoidal categories that play a crucial role in 2-dimensional Conformal Field Theory (2d-CFTs), and that correspond to 3d-TQFTs. Of particular interest are representations of modular tensor categories, and the PI's work here will build on recent joint work with R. Laugwitz and M. Yakimov that constructs canonical representations of braided monoidal categories.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2337830","CAREER: Quantifying congruences between modular forms","DMS","ALGEBRA,NUMBER THEORY,AND COM","08/15/2024","01/18/2024","Preston Wake","MI","Michigan State University","Continuing Grant","Tim Hodges","07/31/2029","$85,593.00","","wakepres@msu.edu","426 AUDITORIUM RD RM 2","EAST LANSING","MI","488242600","5173555040","MPS","126400","1045","$0.00","Number theory is the study of the most basic mathematical objects, whole numbers. Because whole numbers are so fundamental, number theory has connections with all major areas of mathematics. For instance, consider the problem of finding the whole-number solutions to a given equation. One can consider the shape given by the graph of that equation, or the set of symmetries that the equation has, or the function whose coefficients come from counting the number of solutions over a variety of number systems. The geometric properties of this shape, the algebraic properties of these symmetries, and the analytic properties of this function are all intimately related to the behavior of the equation?s whole-number solutions. Number theorists use techniques from each of these mathematical areas, but also, in the process, uncover surprising connections between the areas whereby discoveries in one area can lead to growth in another. One part of number theory where the connections between geometry, algebra, and analysis are particularly strong is in the field of modular forms. The proposed research focuses on an important and well-known type of relation between different modular forms called congruence and aims to compute the number of forms that are congruent to a given modular form and uncover the number-theoretic significance of this computation. Many of the conjectures that drive this project were found experimentally, through computer calculations. The main educational objective is to contribute to the training of the next generation of theoretical mathematicians in computational and experimental methods. To achieve this, the Principal Investigator (PI) will design software modules for a variety of undergraduate algebra and number theory courses that provide hands-on experience with computation. In addition, the PI will supervise undergraduates in computational research experiments designed to numerically verify conjectures made in the project and to explore new directions.<br/><br/>Congruences between modular forms provide a link between two very different types of objects in number theory: algebraic objects, like Galois representations, and analytic objects, like L-functions. This link has been used as a tool for proving some of the most celebrated results in modern number theory, such as the Main Conjecture of Iwasawa theory. The proposed research pushes the study of congruences in a new, quantitative direction by counting the number of congruences, not just determining when a congruence exists. The central hypothesis is that this quantitative structure of congruences contains finer information about the algebraic and analytic quantities involved than the Main Conjecture and its generalizations (such as the Bloch?Kato conjecture) can provide.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2347097","Collaborative Research: Conference: Texas-Oklahoma Representations and Automorphic forms (TORA)","DMS","ALGEBRA,NUMBER THEORY,AND COM","01/01/2024","12/19/2023","Melissa Emory","OK","Oklahoma State University","Standard Grant","Andrew Pollington","12/31/2026","$20,000.00","Maria Fox, Mahdi Asgari","melissa.emory@okstate.edu","401 WHITEHURST HALL","STILLWATER","OK","740781031","4057449995","MPS","126400","7556, 9150","$0.00","This award supports the TORA mathematics conference series. This series consists of annual meetings hosted by the University of North Texas, Oklahoma State University, and the University of Oklahoma on a rotating basis. This award provides support for three weekend conferences, one at the University of North Texas in Spring 2024 (TORA XIII), one at Oklahoma State University in Spring 2025 (TORA XIV), and another at the University of Oklahoma in Spring 2026 (TORA XV). Each conference will feature three prominent guest speakers from outside the Texas-Oklahoma region, in addition to other participants including students, post-doctoral researchers, and junior faculty. Regional graduate students and researchers will also give talks describing their work. These conferences will facilitate collaborations and interactions among the students and researchers in the region who work in the areas of Automorphic Forms, Representation Theory, and Number Theory.<br/><br/>Over the last century, the theories of automorphic forms and representations have grown enormously. Important applications impact various fields of research, ranging from number theory, coding theory, algebraic geometry, and topology to Kac-Moody algebras and quantum field theory. The interplay of automorphic forms and representation theory has been especially fruitful, and many surprising and deep results have emerged. The TORA conference series will emphasize the interplay between automorphic forms and representations, both in the classical and adelic languages, and related topics like analytic number theory and harmonic analysis.<br/><br/><br/><br/>The conference Texas-Oklahoma Representations and Automorphic forms XIII will take place on April 12-14, 2024, at the University of North Texas. Additional information can be found on the conference website: https://www.math.unt.edu/~richter/TORA/TORA13.html<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
+"2402637","Conference: Connecticut Summer School in Number Theory 2024","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/15/2024","04/03/2024","Alvaro Lozano-Robledo","CT","University of Connecticut","Standard Grant","Adriana Salerno","03/31/2025","$29,967.00","Keith Conrad, Jennifer Balakrishnan, Christelle Vincent","alvaro.lozano-robledo@uconn.edu","438 WHITNEY RD EXTENSION UNIT 11","STORRS","CT","062699018","8604863622","MPS","126400","7556","$0.00","The Connecticut Summer School in Number Theory (CTNT 2024) is a conference for advanced undergraduate and beginning graduate students, to be followed by a research conference, taking place at at the University of Connecticut, Storrs campus, from June 10 through June 16, 2024. Even though the northeast of the United States is a hotspot for number theory research, there is no instructional school in number theory that occurs in this region. Undergraduate and beginning graduate students who are interested in number theory may only have had an elementary number theory course during college. The CTNT summer school will achieve several outcomes: expose undergraduate and beginning graduate students to accessible topics that are fundamental to contemporary number theory; provide an environment where students interested in number theory can meet each other and network with students, postdocs, and faculty from institutions where number theory is a strong research area; train a diverse group of students on topics of current importance in number theory; allow advanced undergraduates and beginning graduate students to attend a research conference in number theory; videotape the lectures and post them online at a dedicated website to reach as wide of an audience as possible later: https://ctnt-summer.math.uconn.edu/<br/> <br/>CTNT 2024 will consist of a 4.5-day summer school followed by a 2-day conference. The summer school will have six mini-courses on topics important to contemporary number theory that are not available in a typical college curriculum, such as elliptic curves, reciprocity, adeles and ideles, and class field theory.  The courses will be complemented with course projects, daily invited talks, evening problem sessions, and discussion panels about aspects of graduate school (both for those already in graduate school and those thinking of applying). The conference will consist of several sessions with research talks in number theory, arithmetic geometry, and related topics, and it will be an opportunity for young researchers to present their work.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2401353","Automorphic Forms and the Langlands Program","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/10/2024","Sug Woo Shin","CA","University of California-Berkeley","Continuing Grant","Andrew Pollington","06/30/2027","$87,594.00","","sug.woo.shin@berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","126400","","$0.00","This award concerns research in number theory which studies integers, prime numbers, and solutions of a system of equations over integers or rational numbers following the long tradition from ancient Greeks. In the digital age, number theory has been essential in algorithms, cryptography, and data security. Modern mathematics has seen increasingly more interactions between number theory and other areas from a unifying perspective. A primary example is the Langlands program, comprising a vast web of conjectures and open-ended questions. Even partial solutions have led to striking consequences such as verification of Fermat's Last Theorem, the Sato-Tate conjecture, the Serre conjecture, and their generalizations.<br/><br/>The PI's projects aim to broaden our understanding of the Langlands program and related problems in the following directions: (1) endoscopic classification for automorphic forms on classical groups, (2) a formula for the intersection cohomology of Shimura varieties with applications to the global Langlands reciprocity, (3) the non-generic part of cohomology of locally symmetric spaces, and (4) locality conjectures on the mod p Langlands correspondence. The output of research would stimulate further progress and new investigations. Graduate students will be supported on the grant to take part in these projects. The PI also plans outreach to local high schools which have large under-represented minority populations.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2401098","Groups and Arithmetic","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/10/2024","Michael Larsen","IN","Indiana University","Continuing Grant","Adriana Salerno","06/30/2027","$92,099.00","","larsen@math.indiana.edu","107 S INDIANA AVE","BLOOMINGTON","IN","474057000","3172783473","MPS","126400","","$0.00","This award will support the PI's research program concerning group theory and its applications.  Groups specify symmetry types; for instance, all bilaterally symmetric animals share a symmetry group, which is different from that of a starfish or of a sand dollar.  Important examples of groups arise from the study of symmetry in geometry and in algebra (where symmetries of number systems are captured by ``Galois groups'').  Groups can often be usefully expressed as finite sequences of basic operations,   like face-rotations for the Rubik's cube group, or gates acting on the state of a quantum computer.  One typical problem is understanding which groups can actually arise in situations of interest.  Another is understanding, for particular groups, whether all the elements of the group can be expressed efficiently in terms of a single element or  by a fixed formula in terms of varying elements.  The realization of a particular group as the symmetry group of n-dimensional space is a key technical method to analyze these problems. The award will also support graduate student summer research. <br/><br/>The project involves using  character-theoretic methods alone or in combination with  algebraic geometry, to solve problems about finite simple groups.  In particular, these tools can be applied to investigate  questions about solving equations when the variables are elements of a simple group.  For instance, Thompson's Conjecture, asserting the existence, in any finite simple group of a conjugacy class whose square is the whole group, is of this type.  A key to these methods is the observation that, in practice, character values are usually surprisingly small.  Proving and exploiting variations on this theme is one of the main goals of the project.  One class of applications is to the study of representation varieties of finitely generated groups, for instance Fuchsian groups.  In a different direction, understanding which Galois groups can arise in number theory and how they can act on sets determined by polynomial equations, is an important goal of this project and, indeed, a key goal of number theorists for more than 200 years.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
-"2401380","Quasimaps to Nakajima Varieties","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","04/10/2024","Andrey Smirnov","NC","University of North Carolina at Chapel Hill","Continuing Grant","James Matthew Douglass","05/31/2027","$80,023.00","","asmirnov@live.unc.edu","104 AIRPORT DR STE 2200","CHAPEL HILL","NC","275995023","9199663411","MPS","126400","","$0.00","Counting curves in a given space is a fundamental problem of enumerative geometry. The origin of this problem can be traced back to quantum physics, and especially string theory, where the curve counting provides transition amplitudes for elementary particles. In this project the PI will study this problem for spaces that arise as Nakajima quiver varieties. These spaces are equipped with internal symmetries encoded in representations of quantum loop groups. Thanks to these symmetries, the enumerative geometry of Nakajima quiver varieties is extremely rich and connected with many areas of mathematics. A better understanding of the enumerative geometry of Nakajima quiver varieties will lead to new results in representation theory, algebraic geometry, number theory, combinatorics and theoretical physics. Many open questions in this field are suitable for graduate research projects and will provide ideal opportunities for students' rapid introduction to many advanced areas of contemporary mathematics.<br/> <br/>More specifically, this project will investigate and compute the generating functions of quasimaps to Nakajima quiver varieties with various boundary conditions, uncover new dualities between these functions, and prove open conjectures inspired by 3D-mirror symmetry. The project will also reveal new arithmetic properties of the generating functions via the analysis of quantum differential equations over p-adic fields. The main technical tools to be used include the (algebraic) geometry of quasimap moduli spaces, equivariant elliptic cohomology, representation theory of quantum loop groups, and integral representations of solutions of the quantum Knizhnik-Zamolodchikov equations.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2401049","Conference: Representation Theory and Related Geometry","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/15/2024","04/08/2024","Laura Rider","GA","University of Georgia Research Foundation Inc","Standard Grant","James Matthew Douglass","12/31/2024","$46,000.00","Mee Seong Im","laurajoymath@gmail.com","310 E CAMPUS RD RM 409","ATHENS","GA","306021589","7065425939","MPS","126400","7556","$0.00","This is a grant to support participation in the conference ""Representation theory and related geometry: progress and prospects"" that will take place May 27-31, 2024 at the University of Georgia in Athens, GA. This conference will bring together a diverse set of participants to discuss two key areas of mathematics and their interplay. Talks will include historical perspectives on the area as well as the latest mathematical breakthroughs. A goal of the conference is to facilitate meetings between graduate students, junior mathematicians, and seasoned experts to share knowledge and inspire new avenues of research. In addition to the formally invited talks, the conference will include opportunities for contributed talks and discussion.<br/><br/>The interplay of representation theory and geometry is fundamental to many of the recent breakthroughs in representation theory. Topics will include the representation theory of Lie (super)algebras, and finite, algebraic, and quantum groups; cohomological methods in representation theory; modular representation theory; geometric representation theory; categorification; tensor triangular geometry and related topics in noncommutative algebraic geometry; among others.  More specific topics of interest may include support varieties, cohomology and extensions, endotrivial modules, Schur algebras, tensor triangular geometry, and categorification. The conference website can be found at https://sites.google.com/view/representation-theory-geometry/.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
+"2401380","Quasimaps to Nakajima Varieties","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","04/10/2024","Andrey Smirnov","NC","University of North Carolina at Chapel Hill","Continuing Grant","James Matthew Douglass","05/31/2027","$80,023.00","","asmirnov@live.unc.edu","104 AIRPORT DR STE 2200","CHAPEL HILL","NC","275995023","9199663411","MPS","126400","","$0.00","Counting curves in a given space is a fundamental problem of enumerative geometry. The origin of this problem can be traced back to quantum physics, and especially string theory, where the curve counting provides transition amplitudes for elementary particles. In this project the PI will study this problem for spaces that arise as Nakajima quiver varieties. These spaces are equipped with internal symmetries encoded in representations of quantum loop groups. Thanks to these symmetries, the enumerative geometry of Nakajima quiver varieties is extremely rich and connected with many areas of mathematics. A better understanding of the enumerative geometry of Nakajima quiver varieties will lead to new results in representation theory, algebraic geometry, number theory, combinatorics and theoretical physics. Many open questions in this field are suitable for graduate research projects and will provide ideal opportunities for students' rapid introduction to many advanced areas of contemporary mathematics.<br/> <br/>More specifically, this project will investigate and compute the generating functions of quasimaps to Nakajima quiver varieties with various boundary conditions, uncover new dualities between these functions, and prove open conjectures inspired by 3D-mirror symmetry. The project will also reveal new arithmetic properties of the generating functions via the analysis of quantum differential equations over p-adic fields. The main technical tools to be used include the (algebraic) geometry of quasimap moduli spaces, equivariant elliptic cohomology, representation theory of quantum loop groups, and integral representations of solutions of the quantum Knizhnik-Zamolodchikov equations.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2401351","Quantum Groups, W-algebras, and Brauer-Kauffmann Categories","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","04/12/2024","Weiqiang Wang","VA","University of Virginia Main Campus","Standard Grant","James Matthew Douglass","05/31/2027","$330,000.00","","ww9c@virginia.edu","1001 EMMET ST N","CHARLOTTESVILLE","VA","229034833","4349244270","MPS","126400","","$0.00","Symmetries are patterns that repeat or stay the same when certain changes are made, like rotating a shape or reflecting it in a mirror. They are everywhere in nature, from the spirals of a seashell to the orbits of planets around the sun. They also hide behind mathematical objects and the laws of physics. Quantum groups and Lie algebras are tools mathematicians use to study these symmetries. This project is a deep dive into understanding the underlying structure of these patterns, even when they're slightly changed or twisted, and how they influence the behavior of everything around us. The project will also provide research training opportunities for graduate students.<br/> <br/>In more detail, the PI will develop emerging directions in i-quantum groups arising from quantum symmetric pairs as well as develop applications in various settings of classical types beyond type A. The topics include braid group actions for i-quantum groups; Drinfeld presentations for affine i-quantum groups and twisted Yangians, and applications to W-algebras; character formulas in parabolic categories of modules for finite W-algebras; and categorification of i-quantum groups, and applications to Hecke, Brauer and Schur categories.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2401178","Representation Theory and Symplectic Geometry Inspired by Topological Field Theory","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","04/12/2024","David Nadler","CA","University of California-Berkeley","Standard Grant","James Matthew Douglass","05/31/2027","$270,000.00","","nadler@math.berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","126400","","$0.00","Geometric representation theory and symplectic geometry are two subjects of central interest in current mathematics. They draw original inspiration from mathematical physics, often in the form of quantum field theory and specifically the study of its symmetries. This  has been an historically fruitful direction guided by dualities that generalize Fourier theory. The research in this project involves a mix of pursuits, including the development of new tools and the solution  of open problems. A common theme throughout is finding ways to think about intricate geometric systems in elementary combinatorial terms. The research also offers opportunities for students entering these subjects to make significant contributions by applying recent tools and exploring new approaches. Additional activities  include educational and expository writing on related topics, new interactions between researchers in mathematics and physics, and continued investment in public engagement with mathematics.<br/><br/>The specific projects take on central challenges in supersymmetric gauge theory, specifically about phase spaces of gauge fields, their two-dimensional sigma-models, and higher structures on their branes coming from four-dimensional field theory. The main themes are the cocenter of the affine Hecke category and elliptic character sheaves, local Langlands equivalences and relative  Langlands duality, and the topology of Lagrangian skeleta of Weinstein manifolds. The primary goals of the project include an identification of the cocenter of the affine Hecke category with elliptic character sheaves as an instance of automorphic gluing, the application of cyclic symmetries of Langlands parameter spaces to categorical forms of the Langlands classification, and a comparison of polarized Weinstein  manifolds with arboreal spaces.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2401025","Conference: Algebraic Cycles, Motives and Regulators","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/01/2024","04/10/2024","Deepam Patel","IN","Purdue University","Standard Grant","Andrew Pollington","04/30/2025","$15,000.00","","patel471@purdue.edu","2550 NORTHWESTERN AVE # 1100","WEST LAFAYETTE","IN","479061332","7654941055","MPS","126400","7556","$0.00","This award is to support US participation in Regulators V, the fifth in a series of international conferences dedicated to the mathematics around the theory of regulators, that will take place June 3-13, 2024, at the University of Pisa. The Regulators conferences are an internationally recognized and well-respected series of conferences on topics surrounding the theory of Regulators, many of which have played a key role in recent breakthroughs in mathematics. The conference will bring together a diverse group of participants at a wide range of career stages, from graduate students to senior professors and provide a supportive environment for giving talks, exchanging ideas, and beginning new collaborations. This has traditionally been a fruitful place for early career researchers in these fields to connect with potential collaborators and mentors at other institutions, working on related topics. This award is mainly to support such participants.<br/><br/>Regulators play a central role in algebraic geometry and number theory, being the common thread relating algebraic cycles and motives to number theory and arithmetic. They are the central objects appearing in several well-known conjectures relating L-functions and algebraic cycles, including the Birch--Swinnerton-Dyer conjecture, and conjectures of Deligne, Beilinson, and Bloch-Kato relating special values of L-functions of varieties to algebraic cycles and K-theory. The study of these objects have led to the development of related fields including Iwasawa theory, K-theory, and motivic homotopy theory. They also appear in many areas of mathematics outside algebraic geometry and number theory, most notably in mathematical physics. The topics covered at Regulators V are likely to include recent developments in Iwasawa theory and p-adic L-functions, K-theory, motivic homotopy theory, motives and algebraic cycles, hodge theory, microlocal analysis in characteristic p, and special values of L-functions and additional related areas of research including applications to mathematical physics.<br/><br/><br/>Additional information can be found on the conference website: <br/>http://regulators-v.dm.unipi.it/regulators-v-web.html<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
@@ -51,12 +53,12 @@
 "2401422","Algebraic Geometry and Strings","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/09/2024","Ron Donagi","PA","University of Pennsylvania","Continuing Grant","Adriana Salerno","06/30/2028","$95,400.00","","donagi@math.upenn.edu","3451 WALNUT ST STE 440A","PHILADELPHIA","PA","191046205","2158987293","MPS","126400","","$0.00","Exploration of the interactions of physical theories (string theory and quantum field theory) with mathematics (especially algebraic geometry) has been extremely productive for decades, and the power of this combination of tools and approaches only seems to strengthen with time. The goal of this project is to explore and push forward some of the major issues at the interface of algebraic geometry with string theory and quantum field theory. The research will employ and combine a variety of techniques from algebraic geometry, topology, integrable systems, String theory, and Quantum Field theory. The project also includes many broader impact activities such as steering and organization of conferences and schools, membership of international boards and prize committees, revising Penn?s graduate program, curricular development at the graduate and undergraduate level, advising postdocs, graduate and undergraduate students, editing several public service volumes and editing of journals and proceedings volumes.<br/><br/>More specifically, the project includes, among other topics: a QFT-inspired attack on the geometric Langlands conjecture via non-abelian Hodge theory; a mathematical investigation of physical Theories of class S in terms of variations of Hitchin systems; applications of ideas from supergeometry to higher loop calculations in string theory; exploration of moduli questions in algebraic geometry, some of them motivated by a QFT conjecture, others purely within algebraic geometry; further exploration of aspects of F theory and establishment of its mathematical foundations; and exploration of categorical symmetries and defect symmetry TFTs. Each of these specific research areas represents a major open problem in math and/or in physics, whose solution will make a major contribution to the field.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2349388","Analytic Langlands Correspondence","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/09/2024","Alexander Polishchuk","OR","University of Oregon Eugene","Continuing Grant","James Matthew Douglass","06/30/2027","$82,862.00","","apolish@uoregon.edu","1776 E 13TH AVE","EUGENE","OR","974031905","5413465131","MPS","126400","","$0.00","This is a project in the field of algebraic geometry with connections to number theory and string theory. Algebraic geometry is the study of geometric objects defined by polynomial equations, and related mathematical structures. Three research projects will be undertaken. In the main project the PI will provide a generalization of the theory of automorphic forms, which is an important classical area with roots in number theory. This project provides research training opportunities for graduate students.  <br/><br/>In more detail, the main project will contribute to the analytic Langlands correspondence for curves over local fields. The goal is to study the action of Hecke operators on a space of Schwartz densities associated with the moduli stack of bundles on curves over local fields, and to relate the associated eigenfunctions and eigenvalues to objects equipped with an action of the corresponding Galois group. As part of this project, the PI will prove results on the behavior of Schwartz densities on the stack of bundles near points corresponding to stable and very stable bundles. A second project is related to the geometry of stable supercurves. The PI will develop a rigorous foundation for integrating the superstring supermeasure of the moduli space of supercurves. The third project is motivated by the homological mirror symmetry for symmetric powers of punctured spheres: the PI will construct the actions of various mapping class groups on categories associated with toric resolutions of certain toric hypersurface singularities and will find a relation of this picture to Ozsvath-Szabo's categorical knot invariants.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2401472","Spheres of Influence:  Arithmetic Geometry and Chromatic Homotopy Theory","DMS","ALGEBRA,NUMBER THEORY,AND COM, GEOMETRIC ANALYSIS","09/01/2024","04/10/2024","Jared Weinstein","MA","Trustees of Boston University","Continuing Grant","Adriana Salerno","08/31/2027","$82,195.00","","jsweinst@math.bu.edu","1 SILBER WAY","BOSTON","MA","022151703","6173534365","MPS","126400, 126500","","$0.00","The principal investigator plans to build a bridge between two areas of mathematics:  number theory and topology.  Number theory is an ancient branch of mathematics concerned with the whole numbers and primes.  Some basic results in number theory are the infinitude of primes and the formula which gives all the Pythagorean triples.  Topology is the study of shapes, but one doesn't remember details like length and angles;  the surfaces of a donut and a coffee mug are famously indistinguishable to a topologist.  An overarching theme in topology is to invent invariants to distinguish among shapes.  For instance, a pair of pants is different from a straw because ""number of holes"" is an invariant which assigns different values to them (2 and 1 respectively, but one has to be precise about what a hole is).  The notion of ""hole"" can be generalized to higher dimensions:  a sphere has no 1-dimensional hole, but it does have a 2-dimensional hole and even a 3-dimensional hole (known as the Hopf fibration, discovered in 1931).  There are ""spheres"" in every dimension, and the determination of how many holes each one has is a major unsolved problem in topology.  Lately, the topologists' methods have encroached into the domain of number theory.  In particular the branch of number theory known as p-adic geometry, involving strange number systems allowing for decimal places going off infinitely far to the left, has made an appearance.  The principal investigator will draw upon his expertise in p-adic geometry to make contributions to the counting-holes-in-spheres problem.  He will also organize conferences and workshops with the intent of drawing together number theorists and topologists together, as currently these two realms are somewhat siloed from each other.  Finally, the principal investigator plans to train his four graduate students in methods related to this project.<br/><br/>The device which counts the number of holes in a shape is called the ""homotopy group"".  Calculating the homotopy groups of the spheres is notoriously difficult and interesting at the same time.   There is a divide-and-conquer approach to doing this known as chromatic homotopy theory, which replaces the sphere with its K(n)-localized version.  Here K(n) is the Morava K-theory spectrum.  Work in progress by the principal investigator and collaborators has identified the homotopy groups of the K(n)-local sphere up to a torsion subgroup.   The techniques used involve formal groups, p-adic geometry, and especially perfectoid spaces, which are certain fractal-like entities invented in 2012 by Fields Medalist Peter Scholze.  The next step in the project is to calculate the Picard group of the K(n)-local category, using related techniques.  After this, the principal investigator will turn his attention to the problem known as the ""chromatic splitting conjecture"", which has to do with iterated localizations of the sphere at different K(n).  This is one of the missing pieces of the puzzle required to assemble the homotopy groups of the spheres from their K(n)-local analogues. This award is jointly supported by the Algebra and Number Theory and Geometric Analysis programs.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
-"2401337","Algebraic Cycles and L-functions","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/03/2024","Chao Li","NY","Columbia University","Standard Grant","Adriana Salerno","06/30/2027","$230,000.00","","chaoli@math.columbia.edu","615 W 131ST ST","NEW YORK","NY","100277922","2128546851","MPS","126400","","$0.00","The research in this project concerns one of the basic questions in mathematics: solving algebraic equations. The information of the solutions are encoded in various mathematical objects: algebraic cycles, automorphic forms and L-functions. The research will deepen the understanding of these mathematical objects and the connection between them, especially in high dimensions, which requires solving many new problems, developing new tools and interactions in diverse areas, and appealing to new perspectives which may shed new light on old problems. It will also advance the techniques for understanding the arithmetic of elliptic curves, particularly the Birch and Swinnerton-Dyer conjecture, one of the seven Millennium Prize Problems of the Clay Mathematics Institute. The PI will continue to mentor graduate students, organize conferences and workshops, and write expository articles.  <br/><br/>The PI will work on several projects relating arithmetic geometry with automorphic L-function, centered around the common theme of the generalization and applications of the Gross--Zagier formula. The PI will investigate the Kudla--Rapoport conjecture for parahoric levels. The PI will extend the arithmetic inner product formula to orthogonal groups, and study the Bloch--Kato conjecture of symmetric power motives of elliptic curves and endoscopic cases of the arithmetic Gan--Gross--Prasad conjectures. The PI will also investigate a new arithmetic relative trace formula approach towards a Gross--Zagier type formula for orthogonal Shimura varieties.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2401321","Euler Systems, Iwasawa Theory, and the Arithmetic of Elliptic Curves","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/05/2024","Francesc Castella","CA","University of California-Santa Barbara","Continuing Grant","Adriana Salerno","06/30/2027","$74,832.00","","castella@ucsb.edu","3227 CHEADLE HALL","SANTA BARBARA","CA","931060001","8058934188","MPS","126400","","$0.00","Elliptic curves are a class of polynomial equations (of degree three in two variables) that have been studied for centuries, yet for which many basic questions remain open. For instance, at present there is no proven algorithm to decide whether or not a given elliptic curve has finite or infinitely many rational solutions. Over the past century, mathematicians conjectured that an answer to these questions could be extracted from certain functions of a complex variable, namely the L-function of the elliptic curve. Euler systems and Iwasawa theory are two of the most powerful tools available to date for the study of these and related conjectured links between arithmetic and analysis. This award will advance our understanding of the arithmetic of elliptic curves by developing new results and techniques in Euler systems and Iwasawa theory. The award will also support several mentoring, training, dissemination, and outreach activities.<br/><br/>More specifically, the research to be pursued by the PI and his collaborators will largely focus on problems whose solutions will significantly advance our understanding of issues at the core of the Birch and Swinnerton-Dyer conjecture and related questions in situations of analytic rank 1, and shed new light on the much more mysterious cases of analytic rank 2 and higher. In rank 1, they will prove the first p-converse to the celebrated theorem of Gross-Zagier and Kolyvagin in the case of elliptic curves defined over totally real fields. In rank 2, they will continue their investigations of the generalized Kato classes introduced a few years ago by Darmon-Rotger, establishing new nonvanishing results in the supersingular case. They will also study a systematic p-adic construction of Selmer bases for elliptic curves over Q of rank 2 in connection with the sign conjecture of Mazur-Rubin. For elliptic curves of arbitrary rank, they will establish various non-triviality results of associated Euler systems and Kolyvagin systems, as first conjectured by Kolyvagin and Mazur-Tate.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2400550","Splicing Summation Formulae and Triple Product L-Functions","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/04/2024","Jayce Getz","NC","Duke University","Standard Grant","Andrew Pollington","06/30/2027","$220,000.00","","jgetz@math.duke.edu","2200 W MAIN ST","DURHAM","NC","277054640","9196843030","MPS","126400","","$0.00","This award concerns the Langlands program which has been described as a grand unification theory within mathematics.  In some sense the atoms of the theory are automorphic representations.  The Langlands functoriality conjecture predicts that a collection of natural correspondences preserve these atoms.  To even formulate this conjecture precisely, mathematical subjects as diverse as number theory, representation theory, harmonic analysis, algebraic geometry, and mathematical physics are required.  In turn, work on the conjecture has enriched these subjects, and in some cases completely reshaped them. <br/><br/>One particularly important example of a correspondence that should preserve automorphic representations is the automorphic tensor product. It has been known for some time that in order to establish this particular case of Langlands functoriality it suffices to prove that certain functions known as L-functions are analytically well-behaved. More recently, Braverman and Kazhdan, Ngo, Lafforgue and Sakellaridis have explained that the expected properties of these L-functions would follow if one could obtain certain generalized Poisson summation formulae.  The PI has isolated a particular family of known Poisson summation formulae and proposes to splice them together to obtain the Poisson summation formulae relevant for establishing the automorphic tensor product.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2420166","Conference: The Mordell conjecture 100 years later","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/04/2024","Bjorn Poonen","MA","Massachusetts Institute of Technology","Standard Grant","Andrew Pollington","06/30/2025","$29,970.00","","poonen@math.mit.edu","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","126400","7556","$0.00","The award will support a conference, ``The Mordell conjecture 100 years later'', at the Massachusetts Institute of Technology during the week July 8-12, 2024.  The conference website, showing the list of invited speakers, is https://mordell.org/ .  The Mordell conjecture, proved in 1983, is one of the landmarks of modern number theory.  A conference on this topic is needed now, because in recent years, there have been advances on different aspects of the conjecture, while other key questions remain unsolved.  This would be the first conference to bring together all the researchers coming from these different perspectives.  The conference will feature 16 hour-long lectures, with speakers ranging from the original experts to younger mathematicians at the forefront of current research.  Some lectures will feature surveys of the field, which have educational value especially for the next generation of researchers.  The conference will also feature a problem session and many 5-minute lightning talk slots, which will give junior participants an opportunity to showcase their own research on a wide variety of relevant topics.  The award will support the travel and lodging of a variety of mathematicians including those from underrepresented groups in mathematics and attendees from colleges and universities where other sources of funding are unavailable.  Materials from the lectures, problem session, and lightning talks will be made publicly available on the website, to reach an audience broader than just conference attendees.<br/><br/>The Mordell conjecture motivated much of the development of arithmetic geometry in the 20th century, both before and after its resolution by Faltings.  The conference will feature lectures covering a broad range of topics connected with the Mordell conjecture, its generalizations, and other work it has inspired.  In particular, it will build on recent advances in the following directions: 1) nonabelian analogues of Chabauty's p-adic method; 2) the recent proof via p-adic Hodge theory; 3) uniform bounds on the number of rational points; 4) generalizations to higher-dimensional varieties, studied by various methods: analytic, cohomological, and computational.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2401554","Functoriality for Relative Trace Formulas","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/04/2024","Ioannis Sakellaridis","MD","Johns Hopkins University","Continuing Grant","Andrew Pollington","06/30/2027","$106,185.00","","sakellar@jhu.edu","3400 N CHARLES ST","BALTIMORE","MD","212182608","4439971898","MPS","126400","","$0.00","The Langlands functoriality conjecture, that ""different arithmetic drums share some common eigenfrequencies,"" has immense applications in number theory, among others to the century-old conjectures due to Ramanujan and others about the size of coefficients of special functions called automorphic forms. The PI and his collaborators have broadened this conjecture to the so-called ""relative"" setting, which includes methods of studying special values of L-functions (also called zeta functions), such as in the prominent, and more recent, conjectures of Gan, Gross, and Prasad. The main tool for proving important instances of functoriality so far has been the trace formula, but in its current form it has nearly reached its limits. This project will examine ways to prove these conjectures by use of the idea of quantization, whose origins lie in mathematical physics. This idea will be used to construct novel ways of comparing (relative) trace formulas, drastically expanding their potential reach and applicability. The broader impacts of the project include conference organization and mentoring of graduate students.<br/><br/>The PI has already shown, in prior work, that in some low-rank cases one can establish relative functoriality via some novel ""transfer operators"" between relative trace formulas. Such non-standard comparisons of trace formulas were envisioned in Langlands's ""Beyond Endoscopy"" proposal; the ""relative"" setting allows for more flexibility, and more potential applications, for the exploration of such comparisons. Prior work was focused mostly on the case when the L-groups associated to the relative trace formulas are of rank one. The main goal of this project will be to examine ways to generalize the construction of transfer operators to higher rank. The main idea is to view a trace formula as the quantization of its cotangent stack, which in turn is largely controlled by the L-group. Using natural correspondences between such cotangent stacks, the project aims to construct transfer operators between their quantizations. On a separate track, the project will continue work on the duality of Hamiltonian spaces conjectured in the PI's recent work with Ben-Zvi and Venkatesh, with the aim of extending this duality beyond the hyperspherical setting, and exploring applications for the representation theory of p-adic groups.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2401164","Conference: Latin American School of Algebraic Geometry","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/01/2024","04/10/2024","Evgueni Tevelev","MA","University of Massachusetts Amherst","Standard Grant","Adriana Salerno","04/30/2025","$20,000.00","","tevelev@math.umass.edu","101 COMMONWEALTH AVE","AMHERST","MA","010039252","4135450698","MPS","126400","7556","$0.00","This award will provide travel support for graduate students and early career mathematicians from the United States to participate in the research school ""Latin American School of Algebraic Geometry"" that will take place in Cabo Frio, Brazil from August 12 to 23, 2024, and will be hosted by IMPA (Institute for Pure and Applied Mathematics), a renowned center for mathematical research and post-graduate education founded in 1952 and situated in Rio de Janeiro, Brazil. This will be the fifth edition of the ELGA series. The previous events were held in Buenos Aires (Argentina, 2011), Cabo Frio (Brazil, 2015), Guanajuato (Mexico, 2017), and Talca (Chile, 2019). ELGA is a major mathematical event in Latin America, a focal meeting point for the algebraic geometry community and a great opportunity for junior researchers to network and to learn from the world experts in the field. ELGA workshops are unique in their dedicated efforts to nurture the next generation of leaders in STEM in the Americas. The travel support for U.S. participants from the National Science Foundation will further strengthen the ties between the universities and promote scientific cooperation between future mathematicians in Latin America and the U.S. The website of the conference is https://impa.br/en_US/eventos-do-impa/2024-2/v-latin-american-school-of-algebraic-geometry-and-applications-v-elga/<br/><br/>Algebraic geometry has long enjoyed a central role in mathematics by providing a precise language to describe geometric shapes called algebraic varieties, with applications ranging from configuration spaces in physics to parametric models in statistics. This versatile language is used throughout algebra and has fueled multiple recent advances, not only in algebraic geometry itself but also in representation theory, number theory, symplectic geometry, and other fields. Over the course of two weeks, courses by Cinzia Casagrande (University of Torino, Italy), Charles Favre (École Polytechnique, France), Joaquin Moraga (UCLA, USA), Giancarlo Urzúa (Catholic University, Chile), and Susanna Zimmermann (University of Paris-Saclay, France) will cover a wide range of topics including geometry of Fano manifolds, singularities of algebraic varieties, Cremona groups of projective varieties, Higgs bundles, and geometry of moduli spaces. Each course will include two hours of tutorial sessions coordinated by the course lecturers with the assistance of advanced graduate students participating in the research workshop. Additional talks and presentations by a combination of senior and junior researchers are intended to give a panoramic view of algebraic geometry and its applications.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
+"2401337","Algebraic Cycles and L-functions","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/03/2024","Chao Li","NY","Columbia University","Standard Grant","Adriana Salerno","06/30/2027","$230,000.00","","chaoli@math.columbia.edu","615 W 131ST ST","NEW YORK","NY","100277922","2128546851","MPS","126400","","$0.00","The research in this project concerns one of the basic questions in mathematics: solving algebraic equations. The information of the solutions are encoded in various mathematical objects: algebraic cycles, automorphic forms and L-functions. The research will deepen the understanding of these mathematical objects and the connection between them, especially in high dimensions, which requires solving many new problems, developing new tools and interactions in diverse areas, and appealing to new perspectives which may shed new light on old problems. It will also advance the techniques for understanding the arithmetic of elliptic curves, particularly the Birch and Swinnerton-Dyer conjecture, one of the seven Millennium Prize Problems of the Clay Mathematics Institute. The PI will continue to mentor graduate students, organize conferences and workshops, and write expository articles.  <br/><br/>The PI will work on several projects relating arithmetic geometry with automorphic L-function, centered around the common theme of the generalization and applications of the Gross--Zagier formula. The PI will investigate the Kudla--Rapoport conjecture for parahoric levels. The PI will extend the arithmetic inner product formula to orthogonal groups, and study the Bloch--Kato conjecture of symmetric power motives of elliptic curves and endoscopic cases of the arithmetic Gan--Gross--Prasad conjectures. The PI will also investigate a new arithmetic relative trace formula approach towards a Gross--Zagier type formula for orthogonal Shimura varieties.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2401464","Conference: Solvable Lattice Models, Number Theory and Combinatorics","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","04/09/2024","Solomon Friedberg","MA","Boston College","Standard Grant","James Matthew Douglass","05/31/2025","$22,500.00","","friedber@bc.edu","140 COMMONWEALTH AVE","CHESTNUT HILL","MA","024673800","6175528000","MPS","126400","7556","$0.00","This award supports the participation of US-based researchers in the Conference on Solvable Lattice Models, Number Theory and Combinatorics that will take place June 24-26, 2024 at the Hamilton Mathematics Institute at Trinity College Dublin.  Solvable lattice models first arose in the description of phase change in physics and have become useful tools in mathematics as well. In the past few years a group of researchers have found that they may be used to effectively model quantities arising in number theory and algebraic combinatorics. At the same time, other scholars have used different methods coming from representation theory to investigate these quantities.  This conference will be a venue to feature these developments and to bring together researchers working on related questions using different methods and students interested in learning more about them.<br/><br/>This conference focuses on new and emerging connections between solvable lattice models and special functions on p-adic groups and covering groups, uses of quantum groups, Hecke algebras and other methods to study representations of p-adic groups and their covers, and advances in algebraic combinatorics and algebraic geometry.  Spherical and Iwahori Whittaker functions are examples of such special functions and play an important role in many areas. The website for this conference is https://sites.google.com/bc.edu/solomon-friedberg/dublin2024.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2401114","Parahoric Character Sheaves and Representations of p-Adic Groups","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/09/2024","Charlotte Chan","MI","Regents of the University of Michigan - Ann Arbor","Continuing Grant","James Matthew Douglass","06/30/2027","$105,981.00","","charchan@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","126400","","$0.00","In the past half century, cutting-edge discoveries in mathematics have occurred at the interface of three major disciplines: number theory (the study of prime numbers), representation theory (the study of symmetries using linear algebra), and geometry (the study of solution sets of polynomial equations). The interactions between these subjects has been particularly influential in the context of the Langlands program, arguably the most expansive single project in modern mathematical research. The proposed research aims to further these advances by exploring geometric techniques in representation theory, especially motivated by questions within the context of the Langlands conjectures. This project also provides research training opportunities for undergraduate and graduate students.<br/><br/>In more detail, reductive algebraic groups over local fields (local groups) and their representations control the behavior of symmetries in the Langlands program. This project aims to develop connections between representations of local groups and two fundamental geometric constructions: Deligne-Lusztig varieties and character sheaves. Over the past decade, parahoric analogues of these geometric objects have been constructed and studied, leading to connections between (conjectural) algebraic constructions of the local Langlands correspondence to geometric phenomena, and thereby translating open algebraic questions to tractable problems in algebraic geometry. In this project, the PI will wield these novel positive-depth parahoric analogues of Deligne-Lusztig varieties and character sheaves to attack outstanding conjectures in the local Langlands program.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2411537","Conference: Comparative Prime Number Theory Symposium","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/01/2024","04/05/2024","Wanlin Li","MO","Washington University","Standard Grant","Adriana Salerno","04/30/2025","$10,000.00","","wanlin@wustl.edu","ONE BROOKINGS DR","SAINT LOUIS","MO","63110","3147474134","MPS","126400","7556","$0.00","The workshop Comparative Prime Number Theory Symposium, which is the first scientific event to focus predominantly on this subject, will take place on the UBC--Vancouver campus from June 17--21, 2024. One of the first and central topics in the research of number theory is to study the distribution of prime numbers. In 1853, Chebyshev observed that there seems to be more primes taking the form of a multiple of four plus three than a multiple of four plus one. This phenomenon is now referred to as Chebyshev's bias and its study led to a new branch of number theory, comparative prime number theory. As a subfield of analytic number theory, research in this area focuses on examining how prime counting functions and other arithmetic functions compare to one another. This field has witnessed significant growth and activity in the last three decades, especially after the publication of the influential article on Chebyshev's bias by Rubinstein and Sarnak in 1994.  The primary goal of this award will be to provide participant support and fund US-based early career researchers to attend this unique event, giving them the opportunity to discuss new ideas, advance research projects, and interact with established researchers.<br/><br/>The symposium will bring together many leading and early-career researchers with expertise and interest in comparative prime number theory to present and discuss various aspects of current research in the field, with special emphasis on results pertaining to the distribution of counting functions in number theory and zeros of L-functions, consequences of quantitative Linear Independence, oscillations of the Mertens sum, and the frequency of sign changes. Through this symposium, we will advertise the recently disseminated survey ""An Annotated Bibliography for Comparative Prime Number Theory"" by Martin et al which aims to record every publication within the topic of comparative prime number theory, together with a summary of results, and presenting a unified system of notation and terminology for referring to the quantities and hypotheses that are the main objects of study. Another important outcome of the symposium will be compiling and publicizing a problem list, with the hope of stimulating future research and providing young researchers with potential projects. Information about the conference can be found at the website: https://sites.google.com/view/crgl-functions/comparative-prime-number-theory-symposium<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
@@ -65,10 +67,10 @@
 "2334874","Conference: Pittsburgh Links among Analysis and Number Theory (PLANT)","DMS","ALGEBRA,NUMBER THEORY,AND COM, ANALYSIS PROGRAM","02/01/2024","01/19/2024","Carl Wang Erickson","PA","University of Pittsburgh","Standard Grant","James Matthew Douglass","01/31/2025","$20,000.00","Theresa Anderson, Armin Schikorra","carl.wang-erickson@pitt.edu","4200 FIFTH AVENUE","PITTSBURGH","PA","152600001","4126247400","MPS","126400, 128100","7556","$0.00","This award will support the four-day conference ""Pittsburgh Links among Analysis and Number Theory (PLANT)"" that will take place March 4-7, 2024 in Pittsburgh, PA. The purpose of the conference is to bring together representatives of two disciplines with a shared interface: number theory and analysis. There is a large potential for deeper collaboration between these fields resulting in new and transformative mathematical perspectives, and this conference aims at fostering such an interchange. In particular, the conference is designed to attract PhD students and post-doctoral scholars into working on innovations at this interface. <br/> <br/>To encourage the development of new ideas, the conference speakers, collectively, represent many subfields that have developed their own distinctive blend of analysis and number theory, such as analytic number theory, arithmetic statistics, analytic theory of modular and automorphic forms, additive combinatorics, discrete harmonic analysis, and decoupling. While there have been a wide variety of conferences featuring these subfields in relative isolation, the PIs are excited at PLANT's potential for sparking links among all of these subfields and giving early-career participants the opportunity to be part of this exchange. The conference website is https://sites.google.com/view/plant24/home.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2401041","Conference: Singularities in Ann Arbor","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/01/2024","03/28/2024","Mircea Mustata","MI","Regents of the University of Michigan - Ann Arbor","Standard Grant","Adriana Salerno","04/30/2025","$33,758.00","Qianyu Chen","mmustata@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","126400","7556","$0.00","The conference ""Singularities in Ann Arbor"", scheduled for May 13-17, 2024, at the University of Michigan, Ann Arbor, will explore recent progress in the study of singularities in algebraic geometry. Algebraic geometry, in simple terms, concerns itself with studying geometric objects defined by polynomial equations. This conference will focus on several recent advances concerning singularities: these are points where the geometric objects behave in unexpected ways (such as the bumps or dents on a normally flat surface). Understanding these singularities not only satisfies intellectual curiosity but also plays a crucial role in classifying and comprehending global complex geometric structures. More details about the conference, as well as the list of confirmed lecturers, are available on the conference website, at https://sites.google.com/view/singularitiesinaa.<br/><br/>The conference will feature four lecture series presented by leading experts and rising stars in the field, covering recent advancement related to singularities. These lectures will introduce fresh perspectives and tools, including Hodge Theory, D-modules, and symplectic topology, to address challenging questions in algebraic geometry. The conference aims to make these complex ideas accessible to a younger audience, fostering engagement and understanding among participants.  Additionally, the conference will provide a platform for young researchers to showcase their work through a poster session, encouraging collaboration and discussion among participants.  This award will provide travel and lodging support for about 35 early-career conference participants.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2344680","Conference: Tensor Invariants in Geometry and Complexity Theory","DMS","ALGEBRA,NUMBER THEORY,AND COM, GEOMETRIC ANALYSIS, Algorithmic Foundations","03/15/2024","02/20/2024","Luke Oeding","AL","Auburn University","Standard Grant","James Matthew Douglass","02/28/2025","$40,000.00","","oeding@auburn.edu","321-A INGRAM HALL","AUBURN","AL","368490001","3348444438","MPS","126400, 126500, 779600","7556, 9150","$0.00","The conference Tensor Invariants in Geometry and Complexity Theory will take place May 13-17, 2024 at Auburn University. This conference aims to bring together early-career researchers and experts to study tensor invariants, their appearance in pure algebraic and differential geometry, and their application in Algebraic Complexity Theory and Quantum Information. The workshop will feature talks from both seasoned experts and promising young researchers. The event is designed to facilitate new research connections and to initiate new collaborations. The  conference will expose the participants to state-of-the-art research results that touch a variety of scientific disciplines. The activities will support further development of both pure mathematics and the ""down-stream"" applications in each area of scientific focus (Algebraic and Differential Geometry, Algebraic Complexity, Quantum Information). <br/><br/>The conference is centered on invariants in geometry, divided into three themes: Algebraic and Differential Geometry, Tensors and Complexity, and Quantum Computing and Quantum Information. Geometry has long been a cornerstone of mathematics, and invariants are the linchpins. Regarding Algebraic and Differential Geometry, the organizers are inviting expert speakers on topics such as the connections between projective and differential geometry. Considerations in these areas, such as questions about dimensions and defining equations of secant varieties, have led to powerful tools both within geometry and applications in areas such as computational complexity and quantum information. Likewise, the organizers are inviting application-area experts in Algebraic Complexity and Quantum Information. This natural juxtaposition of pure and applied mathematics will lead to new and interesting connections and help initiate new research collaborations. In addition to daily talks by seasoned experts, the conference will include young researchers in a Poster Session and provide networking opportunities, including working group activities, to help early career researchers meet others in the field, which will provide opportunities for new (and ongoing) research collaborations. It is anticipated that these collaborations will continue long after the meeting is over. The conference webpage is: https://webhome.auburn.edu/~lao0004/jmlConference.html.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
-"2342225","RTG: Numbers, Geometry, and Symmetry at Berkeley","DMS","ALGEBRA,NUMBER THEORY,AND COM, WORKFORCE IN THE MATHEMAT SCI","08/01/2024","03/18/2024","Tony Feng","CA","University of California-Berkeley","Continuing Grant","Andrew Pollington","07/31/2029","$1,196,058.00","Martin Olsson, David Nadler, Sug Woo Shin, Yunqing Tang","fengt@berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","126400, 733500","","$0.00","The project will involve a variety of activities organized around the research groups in number theory, geometry, and representation theory at UC Berkeley. These subjects study the structure and symmetries of mathematical equations, and have applications to (for example) cryptography, codes, signal processing, and physics. There will be an emphasis on training graduate students to contribute to society as scientists, educators, and mentors. <br/><br/>More precisely, RTG will be used to organize annual graduate research workshops, with external experts, as well as weekly research seminars to keep up-to-date on cutting-edge developments. Summer programs on Research Experiences of Undergraduates will provide valuable research exposure to undergraduates, and also mentorship training to graduate students. Postdocs will be hired to help lead these activities. Finally, the project will fund outreach to local schools. At the core of all these activities is the goal of training students and postdocs as strong workforce in their dual roles as mentors and mentees, recruiting students into the ?eld with a good representation of underrepresented groups, and providing a setting for collaboration between all levels and across di?erent areas.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2402436","Conference: Visions in Arithmetic and Beyond","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","03/26/2024","Akshay Venkatesh","NJ","Institute For Advanced Study","Standard Grant","Andrew Pollington","05/31/2025","$44,975.00","Alexander Gamburd","akshay@math.ias.edu","1 EINSTEIN DR","PRINCETON","NJ","085404952","6097348000","MPS","126400","7556","$0.00","This award provides funding to help defray the expenses of participants in the conference ""Visions in Arithmetic and Beyond"" (conference website  https://www.ias.edu/math/events/visions-in-arithmetic-and-beyond ) to be held at the Institute for Advanced Study and Princeton University from June 3 to June 7, 2024. Those speaking at the meeting include the leading researchers across arithmetic, analysis and geometry.<br/><br/>The conference will provide high-level talks by mathematicians who are both outstanding researchers and excellent speakers. These will synthesize and expose a broad range of recent advances in number theory as well as related developments in analysis and dynamics. In addition to the talks by leading researchers there is also time allotted for a session on the best practices for mentoring graduate students and postdocs.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2401152","Conference: Modular forms, L-functions, and Eigenvarieties","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/01/2024","03/26/2024","John Bergdall","AR","University of Arkansas","Standard Grant","Adriana Salerno","11/30/2024","$15,000.00","","bergdall@uark.edu","1125 W MAPLE ST STE 316","FAYETTEVILLE","AR","727013124","4795753845","MPS","126400","7556, 9150","$0.00","This award supports US-based scientists to attend the conference ""Modular Forms, L-functions, and Eigenvarieties"". The event will take place in Paris, France from June 18, 2024, until June 21, 2024. Whole numbers are the atoms of our mathematical universe. Number theorists study why patterns arise among whole numbers. In the 1970's, Robert Langlands proposed connections between number theory and mathematical symmetry. His ideas revolutionized the field. Some of the most fruitful approaches to his ideas have come via calculus on geometric spaces. The conference funded here will expose cutting edge research on such approaches. The ideas disseminated at the conference will have a broad impact on the field. The presentations of leading figures will propel junior researchers toward new theories. The US-based participants will make a written summary of the conference. The summaries will encourage the next generation to adopt the newest perspectives. Writing them will also engender a spirit of collaboration within the research community. The summaries along with details of the events will be available on the website https://www.eventcreate.com/e/bellaiche/.<br/> <br/>The detailed aim of the conference is exposing research on modular forms and L-functions in the context of eigenvarieties. An eigenvariety is a p-adic space that encodes congruence phenomena in number theory. Families of eigenforms, L-functions, and other arithmetic objects find their homes on eigenvarieties. The conference's primary goal is exposing the latest research on such families. The presentations will place new research and its applications all together in one place, under the umbrella of the p-adic Langlands program.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2341365","Conference: Southern Regional Number Theory Conference","DMS","ALGEBRA,NUMBER THEORY,AND COM","02/01/2024","01/19/2024","Gene Kopp","LA","Louisiana State University","Standard Grant","James Matthew Douglass","01/31/2026","$35,000.00","Fang-Ting Tu","gkopp@lsu.edu","202 HIMES HALL","BATON ROUGE","LA","708030001","2255782760","MPS","126400","9150","$0.00","Southern Regional Number Theory Conferences (SRNTCs) are planned to be held in the Gulf Coast region March 9?11, 2024, and in Spring 2025, at Louisiana State University in Baton Rouge. The 2024 conference will be the 10th anniversary of the conference series. The SRNTC series serves as an annual number theory event for the Gulf Coast region. It brings together researchers from the region and beyond to disseminate and discuss fundamental research in various branches of number theory, in turn fostering communication and collaboration between researchers. Local students and early-career researchers attending the conferences are exposed to a wide array of problems and techniques, including specialized topics that may have no local experts at their home institutions. Students and early-career researchers are given opportunities to present their research through contributed talks and to expand their professional network.<br/><br/>SRNTC 2024 will feature about ten invited talks by established experts from four countries, speaking on topics in algebraic number theory, analytic number theory, and automorphic forms. It will also feature about twenty-five contributed talks, mostly by regional graduate students and early-career researchers. Information about SRNTC 2024 and SRNTC 2025, including a registration form and the schedule for each conference, is available at the conference website (https://www.math.lsu.edu/srntc).<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
+"2342225","RTG: Numbers, Geometry, and Symmetry at Berkeley","DMS","ALGEBRA,NUMBER THEORY,AND COM, WORKFORCE IN THE MATHEMAT SCI","08/01/2024","03/18/2024","Tony Feng","CA","University of California-Berkeley","Continuing Grant","Andrew Pollington","07/31/2029","$1,196,058.00","Martin Olsson, David Nadler, Sug Woo Shin, Yunqing Tang","fengt@berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","126400, 733500","","$0.00","The project will involve a variety of activities organized around the research groups in number theory, geometry, and representation theory at UC Berkeley. These subjects study the structure and symmetries of mathematical equations, and have applications to (for example) cryptography, codes, signal processing, and physics. There will be an emphasis on training graduate students to contribute to society as scientists, educators, and mentors. <br/><br/>More precisely, RTG will be used to organize annual graduate research workshops, with external experts, as well as weekly research seminars to keep up-to-date on cutting-edge developments. Summer programs on Research Experiences of Undergraduates will provide valuable research exposure to undergraduates, and also mentorship training to graduate students. Postdocs will be hired to help lead these activities. Finally, the project will fund outreach to local schools. At the core of all these activities is the goal of training students and postdocs as strong workforce in their dual roles as mentors and mentees, recruiting students into the ?eld with a good representation of underrepresented groups, and providing a setting for collaboration between all levels and across di?erent areas.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2333970","Conference: Collaborative Workshop in Algebraic Geometry","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","03/21/2024","Sarah Frei","NH","Dartmouth College","Standard Grant","Andrew Pollington","05/31/2025","$24,400.00","Ursula Whitcher, Rohini Ramadas, Julie Rana","sarah.frei@dartmouth.edu","7 LEBANON ST","HANOVER","NH","037552170","6036463007","MPS","126400","7556, 9150","$0.00","This award supports participants to attend a collaborative algebraic geometry research workshop at the Institute for Advanced Study (IAS) during the week of June 24-28, 2024. The goals of the workshop are to facilitate significant research in algebraic geometry and to strengthen the community of individuals in the field from underrepresented backgrounds. We will place a particular focus on forming connections across different career stages. Participants will join project groups composed of a leader and co-leader together with two to three junior participants and will spend the workshop engaged in focused and substantive research. <br/><br/>The projects to be initiated during this workshop represent a wide range of subfields of algebraic geometry (e.g. intersection theory, toric geometry and arithmetic geometry), as well as connections to other fields of math (e.g. representation theory). Specifically, topics include: abelian covers of varieties, del Pezzo surfaces over finite fields, positivity of toric vector bundles, Chow rings of Hurwitz spaces with marked ramification, Ceresa cycles of low genus curves, and the geometry of Springer fibers and Hessenberg varieties. More information is available at https://sites.google.com/view/wiag2024/.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2349888","Conference: International Conference on L-functions and Automorphic Forms","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/01/2024","03/15/2024","Larry Rolen","TN","Vanderbilt University","Standard Grant","Adriana Salerno","03/31/2025","$25,000.00","Jesse Thorner, Andreas Mono","larry.rolen@vanderbilt.edu","110 21ST AVE S","NASHVILLE","TN","372032416","6153222631","MPS","126400","7556","$0.00","This award provides support for the conference entitled ""International Conference on L-functions and Automorphic Forms'', which will take place at Vanderbilt University in Nashville, Tennessee on May 13--16 2024. This is part of an annual series hosted by Vanderbilt, known as the Shanks conference series. The main theme will be on new developments and recent interactions between the areas indicated in the title. The interplay between automorphic forms and L-functions has a long and very fruitful history in number theory, and bridging both fields is still a very active area of research. This conference is oriented at establishing and furthering dialogue on new developments at the boundary of these areas. This will foster collaboration between researchers working in these fields.<br/> <br/>One beautiful feature of modern number theory is that many problems of broad interest, in areas of study as diverse as arithmetic geometry to mathematical physics, can be solved in an essentially optimal way if the natural extension of the Riemann hypothesis holds for L-functions associated to automorphic representations. Although many generalizations and applications around L-functions have have already been worked out, there are still various fundamental open problems among them to tackle, including bounds for and the value distribution of L-functions. The former is related to the pursuit of so-called sub-convexity bounds for L-functions. The latter is related to the Birch and Swinnterton-Dyer conjecture (another ?Millenium problem? posed by the Clay Mathematics institute). These pursuits are closely connected with the Langlands program, a ?grand unifying theory? relating automorphic forms. Further details can be found on the conference website https://my.vanderbilt.edu/shanksseries/.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2400006","Conference: Underrepresented Students in Algebra and Topology Research Symposium (USTARS)","DMS","INFRASTRUCTURE PROGRAM, ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","03/15/2024","03/12/2024","Ryan Moruzzi","CA","California State University, East Bay Foundation, Inc.","Standard Grant","Adriana Salerno","02/28/2025","$36,000.00","Christopher ONeill, Robyn Brooks","ryan.moruzzi@csueastbay.edu","25800 CARLOS BEE BLVD","HAYWARD","CA","945423000","5108854212","MPS","126000, 126400, 126700","7556","$0.00","This award will support the Underrepresented Students in Topology and Algebra Research Symposium (USTARS). A goal of this conference is to highlight research being conducted by underrepresented students in the areas of algebra and topology. At this unique meeting, attendees are exposed to a greater variety of current research, ideas, and results in their areas of study and beyond. Participants are also given the opportunity to meet and network with underrepresented professors and students who may later become collaborators and colleagues. This is particularly important for students with great academic potential who do not attend top-tier research institutions; students that are often overlooked, despite a strong faculty and graduate student population. Furthermore, USTARS promotes diversity in the mathematical sciences by encouraging women and minorities to attend and give talks. Participants of USTARS continue to influence the next generation of students in positive ways by serving as much needed mentors and encouraging students in the mathematical sciences to advance themselves and participate in research and conference events. USTARS exposes all participants to the research and activities of underrepresented mathematicians, encouraging a more collaborative mathematics community. <br/><br/>The Underrepresented Students in Topology and Algebra Research Symposium (USTARS) is a project proposed by a group of underrepresented young mathematicians. The conference organizing committee is diverse in gender, ethnicity, and educational background, and is well-positioned to actively encourage participation by women and minorities. The symposium includes networking sessions along with research presentations. Speakers will give 30-minute parallel research talks. Graduate students will give at least 75% of these presentations. Two distinguished graduate students and one invited faculty member are chosen to give 1-hour presentations and a poster session featuring invited undergraduates is also planned. Additionally, a discussion panel and creative math session will provide networking, guidance, and mentorship opportunities from past USTARS participants that have transitioned to full-time faculty positions. The conference website is https://www.ustars.org/.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
diff --git a/Applied-Mathematics/Awards-Applied-Mathematics-2024.csv b/Applied-Mathematics/Awards-Applied-Mathematics-2024.csv
index bc4706f..037271e 100644
--- a/Applied-Mathematics/Awards-Applied-Mathematics-2024.csv
+++ b/Applied-Mathematics/Awards-Applied-Mathematics-2024.csv
@@ -1,12 +1,20 @@
 "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract"
+"2408098","Singularity Formation in Fluid Mechanics and Related Equations","DMS","APPLIED MATHEMATICS","06/01/2024","05/15/2024","Jiajie Chen","NY","New York University","Standard Grant","Pedro Embid","05/31/2027","$159,956.00","","jiajie.chen@cims.nyu.edu","70 WASHINGTON SQ S","NEW YORK","NY","100121019","2129982121","MPS","126600","","$0.00","The Euler and the Navier-Stokes equations are the most established models in fluid dynamics. Scientists and engineers apply these equations to model various phenomena, including weather patterns, ocean currents, flows around vehicles, aircraft, and ships, as well as blood flow. Mathematicians and physicists believe that understanding the solutions to these equations can lead to an explanation for turbulence. Despite their wide range of applications, there is no theoretical guarantee that smooth solutions to these equations can exist for all time. Mathematically, proving whether smooth solutions to these equations without external forces exist for all time or can break down in finite time has been a longstanding open problem. The potential breakdown mechanism also remains elusive for several related equations with a wide range of applications. The goal of this research is to investigate the potential breakdown mechanism for various equations and develop analytic and numeric tools that provide a theoretical understanding of these mechanisms. This award will also provide opportunities for students to be involved in the latest developments from this research through topics courses and research projects.<br/><br/>The project aims to understand whether the incompressible 3D Euler equations and related equations could develop a finite time singularity from a smooth initial condition with finite energy. Our approach builds on PI's recent works on singularity formation in incompressible fluids and the self-similar method for finite time blowup, which consists of the following three steps. Firstly, we construct an approximate blowup profile, which can be obtained either analytically or numerically. Secondly, we impose suitable normalization conditions and prove the nonlinear stability of the approximate blowup profile. Thirdly, we choose a suitable perturbation to construct initial data with desired property and obtain finite time blowup using a rescaling relation. Additionally, the project seeks to develop a novel approach for the stability analysis in the self-similar variables that is robust enough to be applied to study a larger class of nonlinear partial differential equations.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
+"2404535","Topics in Geometrical Optics and Kinematics: Billiard Models and Tire Track Geometry","DMS","APPLIED MATHEMATICS","06/01/2024","05/15/2024","Serge Tabachnikov","PA","Pennsylvania State Univ University Park","Standard Grant","Stacey Levine","05/31/2027","$300,000.00","","tabachni@math.psu.edu","201 OLD MAIN","UNIVERSITY PARK","PA","168021503","8148651372","MPS","126600","","$0.00","This project comprises two topics: billiard models and geometrical optics, and models of vehicle motion and tire track kinematics. The first part of the project addresses fundamental challenges of ray optics and mathematical billiards that model mechanical systems with elastic collision, such as the ideal gas. Geometrical optics provide a good approximation for many applications, such as trapping rays of light and storing solar energy, invisibility, and laser beam shaping. The second part addresses vehicle kinematics, studied both theoretically and via computer experiments.  Applications include control of tractors with many trailers, preventing driving hazard, motion planning for robots, flotation theory, such as the stability of floating bodies, and modeling of the Josephson effect that plays an essential role in constructing quantum-mechanical circuits. This project will also contribute to the training of graduate researchers.<br/><br/>The mathematical scope of this project is closely related with the theory of completely integrable systems. The billiard (optical) reflection is a symplectic transformation of the space of oriented lines (rays of light), making it possible to use methods of Hamiltonian dynamics and symplectic topology in the study of billiards. For example, the known designs of optical traps for parallel beams of light make use of the complete integrability of the billiard systems inside quadratic surfaces. The second part of the project concerning models of vehicle motion involves methods of sub-Riemannian geometry and Hamiltonian mechanics. A relation with the theory of completely integrable systems is manifested in the fact that the optimal vehicle trajectories, and also the sections of the cylindrical bodies that float in equilibrium in all positions, have the shape of solitons of the filament equation, a well-studied completely integrable system that models the motion of fluid and gas vortices.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2408793","Anisotropic Inverse Problems: Nonlocality, Nonlinearity, and High Frequencies","DMS","APPLIED MATHEMATICS","07/01/2024","05/14/2024","Katya Krupchyk","CA","University of California-Irvine","Standard Grant","Stacey Levine","06/30/2027","$270,000.00","","katya.krupchyk@uci.edu","160 ALDRICH HALL","IRVINE","CA","926970001","9498247295","MPS","126600","","$0.00","Inverse problems arise when measurements obtained from the exterior or boundary of a medium are employed to unveil the properties of its inaccessible interior. This framework is ubiquitous across various scientific and technological disciplines, encompassing fields such as medical imaging, atmospheric remote sensing, geophysics, and non-destructive evaluation. In many practical scenarios, medium parameters exhibit anisotropy, meaning they depend not only on position but also on direction. Examples include conductivity in muscle tissue in human bodies, electromagnetic parameters in crystals, composite materials like fiber-reinforced polymers, and seismic wave propagation in the Earth. The project aims to develop novel mathematical methods for investigating inverse problems related to the recovery of anisotropic medium parameters from measurements taken at the exterior or boundary. A particular focus of the project is on determining parameters in models involving long-range interactions, prevalent in phenomena from anomalous diffusion to random processes with jumps, with broad applications spanning image processing, fluid dynamics, biophysics, network science, epidemiology, and finance. Additionally, the project places significant emphasis on providing educational training for graduate students.<br/><br/>The project leverages nonlocality, nonlinearity, and high frequencies as powerful tools to tackle significant and challenging inverse problems in anisotropic media. It is organized around four pivotal research topics. The first topic concerns inverse problems for elliptic partial differential operators at a large but fixed frequency. The goal is to solve important inverse problems for both linear and nonlinear elliptic operators at a large but fixed frequency in a geometric setting where the corresponding inverse problems at zero frequency are wide open and seem difficult to reach. The second topic focuses on inverse problems for nonlocal elliptic operators, with a particular emphasis on the fractional counterpart of the Calderon problem. The aim is to recover the coefficients of nonlocal operators based on measurements taken in exterior regions. The inherent nonlocality of these operators renders inverse problems more tractable than their local counterparts. The third topic deals with inverse problems for significant nonlinear hyperbolic and elliptic partial differential equations, encountered in physical models. The primary objective is to recover the leading terms that govern the underlying geometry. Finally, the fourth topic addresses inverse problems for both linear and nonlinear perturbations of biharmonic operators, with applications ranging from elasticity theory to conformal geometry.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2406852","Dynamics of Fluids with Singular Interfaces","DMS","APPLIED MATHEMATICS","09/01/2024","05/14/2024","Daniel Ginsberg","NY","CUNY Brooklyn College","Standard Grant","Pedro Embid","08/31/2027","$167,711.00","","daniel.ginsberg@brooklyn.cuny.edu","2900 BEDFORD AVE","BROOKLYN","NY","112102850","7189515622","MPS","126600","","$0.00","In many problems of physical importance, such as the modeling of hot plasmas, the study of the gravitational collapse of stars, or the motion of waves on the surface of the ocean, one encounters fluids surrounded by an interface which is not prescribed ahead of time but instead is free to move along with the fluid. The main mathematical difficulty in these problems lies in understanding the interplay between the dynamics of the fluid and the geometry of the interface. The aim of this project is to develop tools for the study of these problems and to deepen our knowledge of how these interfaces influence the dynamics of fluid models. This award will also provide opportunities for the involvement of undergraduate students in the research projects.  <br/><br/>This award will develop new mathematical tools to tackle problems involving free-surface fluid flows. The first project concerns the study of plasmas in the laboratory setting and is connected with the problem of ""magnetic confinement fusion"", which seeks to control a hot plasma by using powerful magnetic fields for the purposes of harnessing fusion reactions in the core. The mathematical challenge is to identify and construct magnetic fields which are effective at confining hot plasmas. The difficulty is that generic plasma configurations can possess a complicated mixture of invariant surfaces and chaotic regions. The second project concerns the long-time dynamics of self-gravitating fluids. One major obstruction to understanding the long-time behavior of these objects is the existence of a large and complicated family of periodic solutions. The PI will study the stability of these objects as the next step towards understanding the long-time behavior of liquids with free boundary.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
+"2407290","Quantum Hall Fractions and Frames","DMS","APPLIED MATHEMATICS","07/01/2024","05/15/2024","Martin Fraas","CA","University of California-Davis","Continuing Grant","Dmitry Golovaty","06/30/2027","$119,723.00","","mfraas@ucdavis.edu","1850 RESEARCH PARK DR STE 300","DAVIS","CA","956186153","5307547700","MPS","126600","7203","$0.00","This project continues an interdisciplinary endeavor in physics, mathematics, and engineering to deepen our understanding of the quantum Hall effect (QHE) - a phenomenon in which conductance of an electron gas at low temperatures and strong magnetic fields exhibits a unique, staircase-like behavior. The precision of this effect is so remarkable (accurate to one part in a billion) that it underpins the modern metrological definitions of the kilogram and the ampere. The project aims to bridge a crucial gap in the current understanding of the QHE, specifically the lack of microscopic mathematical theory explaining 'anyons' in the fractional quantum Hall effect. Developing such a theory could advance efforts to construct and operate topological quantum computers. Furthermore, the investigator commits to training a new generation of scientists by involving graduate and undergraduate students in cutting-edge research in quantum information and engineering, promoting educational advancement and diversity in STEM fields. Through these efforts, the project not only advances scientific knowledge but also helps maintain a skilled workforce. <br/><br/>The project focuses on the theory of integer and fractional QHE. While our understanding of integer QHE is quite robust, there remain several profound mathematical problems that have yet to be answered. Conversely, our comprehension of fractional QHE is limited, and there is no microscopic theory of anyons in the fractional quantum Hall effect - such a theory is highly relevant for applications in topological quantum computation. This project aims to advance our understanding of the fractional case and address open problems in the integer case. The project comprises two parts: (A) fractions in QHE and (B) frustration-free models of QHE. A significant problem in the theory of fractional QHE is explaining which fractions are admissible. Notably, a fractional Hall conductance of one half is not experimentally observed (is not admissible), while one third is. Numerous competing theories attempt to explain admissible fractions, but even within the realm of theoretical physics, there is no definitive answer to this problem. At a mathematical level of rigor, nothing is known. The investigator will study a new, symmetry-based explanation and further aims to make this explanation mathematically rigorous. The idea is to relate admissible fractions to symmetry constraints on a modular tensor category that describes anyonic excitations of the system. All exactly solvable models of anyons are frustration-free; however, none of these models describe the QHE. In (B), the goal is to demonstrate that this is not a coincidence and that all frustration-free models have zero Hall conductance. The investigator aims to establish a connection to the theory of frames and use this connection to prove the conjecture. The investigator will employ a diverse combination of mentoring activities to guide mentees' individual research processes and provide them with opportunities to participate in more advanced work. The project also includes sub-projects for undergraduate students aimed at filling a gap in research experience opportunities for undergraduate students at UC Davis.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
+"2407080","Soliton Gases for the Focusing Nonlinear Schroedinger Equation and Other Integrable Systems: Theory and Applications","DMS","APPLIED MATHEMATICS","09/01/2024","05/15/2024","Alexander Tovbis","FL","The University of Central Florida Board of Trustees","Continuing Grant","Dmitry Golovaty","08/31/2027","$172,211.00","","alexander.tovbis@ucf.edu","4000 CENTRAL FLORIDA BLVD","ORLANDO","FL","328168005","4078230387","MPS","126600","","$0.00","Nonlinear integrable equations play increasingly important role in the modelling of various phenomena in natural sciences and engineering. This fact stems from two key observations: a) these equations can capture various physical phenomena that cannot be described by simpler models, and b) these equations allow for various classes of solutions that can be calculated in explicit form. For example, the Nonlinear Schroedinger Equation (NLS), is widely used to model wave propagation in weakly nonlinear dispersive media (fiber optics, deep water gravity waves) when dissipation can be neglected. It was observed that solitons, which are the most celebrated explicit solutions of integrable systems, can be viewed as ?""quasi particles"" of complex statistical objects called soliton gases. The main idea of this project is to model random nonlinear waves, which are frequently encountered in natural phenomena, with large random ensembles of solitons. Ultimately, the project aims to enhance our ability to predict and, in some cases, to control random nonlinear waves, as well as to derive their statistical characteristics. Being by nature a mixture of pure and applied mathematics and also leading to new lab experiments, the work on the project could benefit by cross pollination of ideas and methods originating from different parts of nonlinear waves research community. The project is expected to advance our general knowledge of random nonlinear waves, including the rogue waves (RW), and to improve methods of prediction of the latter. In the fiber optics, the results of the project may help to model and, perhaps, to control the evolution of noise in NLS governed nonlinear fibers. The project will also serve as a vehicle for training graduate and undergraduate students, including minorities, as well as postdocs.<br/> <br/>The main goals of this project are a) development of a rigorous spectral theory for soliton gases for integrable equations (KdV, fNLS, sine-Gordon, etc.), and b) statistical characterization of such soliton gases. The work in part a) requires rigorous derivation and analysis of the nonlinear dispersion relations (NDR), which describe spectral characteristics of the gases, as well as construction of explicit families of solutions to NDR (condensates, periodic gases, etc.) that can be of special interest in applications. The recent observation by the principal investigator (PI) that the NDR can be considered as a large genus (``thermodynamic"") limit of Riemann Bilinear Identities on some special sequences of Riemann surfaces reveals a deep and intriguing connections between the algebraic geometry and the spectral theory of soliton gases for integrable equations, which the PI is interested in understanding and analyzing. This approach requires some new potential theory methods for solving minimization problems on Riemann surfaces. Calculation of important statistical characteristics (probability density function, power spectrum, kurtosis, etc.) of the soliton gases from part b) contains both analytical and numerical components. The obtained theoretical results will lead to laboratory experiments in collaboration with leading experts in the area of experimental fiber optics and water waves.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
+"2405326","Hydrodynamic Theory of Environmental Averaging and Self-organization","DMS","APPLIED MATHEMATICS","06/01/2024","05/15/2024","Roman Shvydkoy","IL","University of Illinois at Chicago","Standard Grant","Pedro Embid","05/31/2027","$280,000.00","","shvydkoy@math.uic.edu","809 S MARSHFIELD AVE M/C 551","CHICAGO","IL","606124305","3129962862","MPS","126600","","$0.00","Many mathematical models of swarming behavior reflect the tendency of every agent to adjust its velocity to an averaged direction of motion of the crowd around.  Such examples are abundant in biology, dynamics of human crowds, social networking, and even in technology (coordinated fight of an escort of UAVs or satellite navigation). Although the laws that describe the average may not be given explicitly, most adhere to a few basic principles. First, agents react more to the closest neighbors, and second, the density of the swarm plays a constructive role in defining particular communication rules. Such rules give rise to what is called ""environmental averaging"".   Large swarms regulated by environmental averaging are governed by models similar to those we use to study motion of a liquid like water or gas.  Thanks to this connection a new trend emerged in the studies of collective behavior which looks at these phenomena from the point of view of hydrodynamic modeling. This project proposes to analyze hydrodynamic collective models aiming at understanding their fundamental mathematical properties and with a view towards their applications to collective phenomena. In parallel with the research effort, the project will involve students and researchers through a working group seminar on the mathematics of collective behavior at the University of Illinois at Chicago. <br/><br/>Central to the project will be the development of a general methodology that unifies numerous models. Focus will be placed on justification of a class hydrodynamic models called Euler Alignment System and its kinetic counterpart the Fokker-Planck-Alignment model.  We aim to provide a justification for such systems going from particle dynamics through the mean-field limit and into macroscopic description through various hydrodynamic limits. It will be possible to obtain new barotropic pressure laws which have proved to be useful in real life modeling. Exploiting parallels with the classical theory of fluids we plan to study collective outcomes described by natural thermodynamic equilibria of the system, and to bring the regularity theory of such systems to the level usable in the studies of long-time behavior of the system.  Applications of this research are numerous including opinion mean-field games, segregation modeling, and modeling of turbulent phenomena in 2D inviscid fluids.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2407235","Free Boundary Geometry in Heterogeneous Media","DMS","APPLIED MATHEMATICS","07/01/2024","05/14/2024","William Feldman","UT","University of Utah","Continuing Grant","Dmitry Golovaty","06/30/2027","$184,162.00","","feldman@math.utah.edu","201 PRESIDENTS CIR","SALT LAKE CITY","UT","841129049","8015816903","MPS","126600","","$0.00","Free boundary problems arise in the mathematical modelling of physical systems with a phase interface.  Well-known, and perhaps familiar, examples include the Stefan problem for melting and freezing of ice in water and the capillary problem describing the shapes of water droplets on a car window or a leaf.  In these problems it is very important to understand the effects of heterogenous media. Microscopic structure plays a major role in determining the macroscopic physics, for example whether a water droplet will ""stick"" to a surface (due to contact angle hysteresis) or roll off (low hysteresis and/or superhydrophobicity). In mathematical terms such interface problems lie at the intersection of several fields: partial differential equations (PDE), geometry, and probability / statistical physics. This project aims to advance the theory of phase interfaces in heterogeneous media by developing new techniques which make connections between these distinct mathematical fields.  The project will contribute to the development of STEM workforce and STEM education through training of graduate students and postdoctoral researchers.<br/><br/>This project will study free boundary problems in heterogeneous media at micro and macro scales, especially as related to problems of capillarity and wetting.   The two main goals are: (1) to develop a theory of large-scale regularity for one- and two-phase free boundary problems and obstacle problems in periodic and random media, (2) to derive and study models for the rate independent evolution of capillary drops under the effects of contact angle hysteresis.  Quantitative results in homogenization and hydrodynamic limits enable more efficient computations which can be rigorously validated.  The large-scale regularization properties of elliptic and parabolic PDE in periodic and random media is central in the study of quantitative homogenization.  Much less is known in the context of phase interfaces or free boundaries.  This project will advance the quantitative homogenization theory of free boundaries and interfaces by studying several important model problems. In the theory of wetting on a rough surface, a rigorous mathematical formulation in terms of calculus of variations and homogenization theory can clarify the meaning of ambiguous physical models for computing effective contact angles. This project will enhance the understanding of these models both from a theoretical and computational perspective.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2406313","Time Harmonic Inverse Scattering for Linear and Nonlinear Media","DMS","APPLIED MATHEMATICS","08/01/2024","05/14/2024","Fioralba Cakoni","NJ","Rutgers University New Brunswick","Standard Grant","Stacey Levine","07/31/2027","$269,999.00","","fc292@math.rutgers.edu","3 RUTGERS PLZ","NEW BRUNSWICK","NJ","089018559","8489320150","MPS","126600","","$0.00","In numerous domains of national significance, such as renewable energy, non-invasive medical diagnosis, underground exploration, infrastructure integrity, and the manufacturing of novel materials including 3-D printing, the ability to conduct fast imaging using electromagnetic, acoustic, or elastic waves is crucial. Developing effective methods for testing complex materials to detect structural defects or identify unknown targets efficiently and with minimal a priori information is highly desirable. This need is particularly pronounced for materials exhibiting directional properties, multi-periodicities with non-commensurable periods, nonlinear interactions with probing waves, or peculiar geometric structures, all prevalent in modern applications across the mentioned domains. This project involves the development of novel techniques in inverse scattering theory to address contemporary imaging challenges, aiming for reliable target signatures or useful information about examined objects in computationally efficient ways. The objective is to reduce reliance on a priori information describing the physics and geometry of targets, as well as on mathematical and computational complexities arising from complex background environments.  Graduate students will be trained and participate in this research. <br/><br/>This project will investigate a non-iterative approach for solving inverse scattering problems for both linear and nonlinear inhomogeneous media.   The generalized linear sampling method and interior eigenvalues form the unified mathematical framework for four interconnected projects. 1) Imaging of Inhomogeneous Media with Interior Eigenvalues: Motivated by the theory of transmission eigenvalues, the investigator and collaborators have developed a framework for modifying the scattering data, leading to new eigenvalue problems related to injectivity of the relative scattering operator. These eigenvalues are determined from scattering data and show versatile potential to image changes/faults in the media. The goal of this project is to address mathematical and computational questions in this framework to broaden the applicability of these techniques to anisotropic/absorbing/dispersive media, meta-surfaces, and clusters of defects. 2) Transmission Eigenvalues and Non-scattering Phenomena: A fundamental challenge in scattering theory is whether incoming time harmonic waves at a particular wave number are not scattered by a given inhomogeneity. The investigator will address mathematical questions on this topic involving non-selfadjoint spectral theory and free boundary regularity. These questions are important in applications since at a non-scattering wave number, the scattering operator is not injective. 3) Qualitative and Spectral Imaging Approach for Nonlinear Media: This project aims to establish mathematical foundations of inverse scattering for second-order harmonic generation in nonlinear optics as well as to develop the generalized linear sampling method and related spectral imaging for this model. This approach is promising for nonlinear models since it does not require solving the nonlinear partial differential equations. 4) Scattering by Almost-periodic Layers and Imaging of Local Defects: Periodicity plays an important role in the engineering of exotic materials in contemporary applications. Mathematically, almost periodic coefficients in the equations that govern wave propagation are viewed as traces along a hyperplane with an irrational normal of higher-dimensional periodic functions. This leads to a degenerate augmented principal differential operator in the model. Having understood the direct scattering problem, the investigator plans to extend the generalized linear sampling method to reconstruct local perturbation within an almost periodic layer without knowing a priori the almost periodic coefficients.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
+"2406762","Mean Field Optimal Control","DMS","APPLIED MATHEMATICS","07/01/2024","05/15/2024","Halil Soner","NJ","Princeton University","Standard Grant","Pedro Embid","06/30/2027","$320,000.00","","soner@princeton.edu","1 NASSAU HALL","PRINCETON","NJ","085442001","6092583090","MPS","126600","075Z","$0.00","Differential games have a complex and flexible structure making it a central modeling tool for diverse phenomena arising in social sciences, economics as well as engineering.  Despite its appeal, this complexity and flexibility also often makes its mathematical analysis intractable. In cases when the game is played by a large number of identical agents, mean field paradigm widely employed in physics offers a simplifying approach without compromising its modeling potential.  This new perspective has been actively studied over the past decade and proved to be effectively applicable across various fields.  Additionally, as in the mean field regime the players have small impact on the macro behavior of the system, it becomes feasible to coordinate their actions through a central planner providing equilibria that are beneficial to all. This project is centered around these models that are centrally controlled.  While in some cases this is the natural setting, games that have potential structure are also intrinsically connected to these mean field control problems. This project also provides opportunities for the involvement of students in the research.<br/><br/>Technically, the main feature of mean field type optimization is the dependence of its evolution and cost, not only on the position of the state, but also on its probability distribution, making the set of distributions its state space. Thus, the dynamic programming approach results in nonlinear partial differential equations set in the spaces of probability measures. For games these are coupled Hamilton-Jacobi and Fokker-Planck-Kolmogorov systems. For mean field control however, the differential equations characterizing the minimal value are naturally set in the Wasserstein space of probability measures with finite second moments, and they are not expected to admit classical solutions.  Towards the central goal of building an efficient theory for these equations, this project aims to develop a complete theory for the associated dynamic programming equation for mean field control, to study the potential games in detail, and to establish efficient numerical approaches using modern optimization packages with theoretical guarantees based on tools from statistical machine learning.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
+"2406623","Dynamics of reaction-diffusion equations on networks and other spatially extended systems","DMS","APPLIED MATHEMATICS","07/01/2024","05/15/2024","Matt Holzer","VA","George Mason University","Standard Grant","Stacey Levine","06/30/2027","$269,996.00","","mholzer@gmu.edu","4400 UNIVERSITY DR","FAIRFAX","VA","220304422","7039932295","MPS","126600","","$0.00","Physical systems which can be modeled by differential equations relying upon an interplay between spatially organized interactions and homogeneous reaction dynamics span a wide range of applications in biology, ecology, physics, and engineering. This project will contribute theoretical and computational approaches for understanding the dynamics of such reaction-diffusion systems.  One theme of this research is understanding how complexities in the spatial coupling of components affect the dynamics of these systems.  This complexity could take the form of network-based interactions of components or it could consist of understanding the role of spatial barriers for which the rate of diffusion or reaction is different from that of the bulk of the domain.  Outcomes will include mathematical results validating certain reduced systems, modeling and analysis of several applied problems, as well as the development of rigorous computational methods for the study of traveling interfaces.   The project will also contribute to the training of PhD and undergraduate researchers.<br/><br/>Three specific project areas are to be considered.  The first revolves around the analysis of reaction-diffusion equations defined on networks.  When the number of components is large, it is often convenient to pass to a mean-field limit where the discrete graph is replaced by a more tractable nonlocal equation.  The goal of this project is to contribute theoretical results relating the nonlocal equation and the discrete system thereby validating the use of the nonlocal equation.  The second project involves the development of validated numerical techniques for the study of fronts propagating into unstable states.  The primary challenge in this analysis is the appearance of repeated eigenvalues and resonances in the linearization of the traveling wave equation near the unstable state.  The third project involves partial differential equation models defined on spatial domains with dynamical barriers.  Focusing on the dynamics near unstable states, the project will quantify how the dynamics within these barriers affect the evolution of the overall system and speed of invasion of the unstable state.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2407046","Transport of Particles in Heterogeneous Media","DMS","APPLIED MATHEMATICS","06/01/2024","05/14/2024","Alexei Novikov","PA","Pennsylvania State Univ University Park","Continuing Grant","Stacey Levine","05/31/2027","$157,975.00","","anovikov@math.psu.edu","201 OLD MAIN","UNIVERSITY PARK","PA","168021503","8148651372","MPS","126600","","$0.00","Heterogeneous environments are ubiquitous, with examples including ocean flows, atmospheric turbulence, oil-bearing sands, and biological tissues. Understanding the overall properties of such media is relevant to virtually every branch of science and engineering, especially computer science, materials science, chemical engineering, geophysics, medical imaging, and fluid dynamics. The first part of this project concerns changes in salinity or chlorofluorocarbon on the surface of the ocean. Oceanic vortices may dramatically change mixing rates of various chemical compounds. The aim of this project is to estimate these rates using simpler mathematical models to illuminate the mechanisms present in the full system. The second goal of this project is related to speeding up Markov Chain Monte Carlo algorithms. Markov Chain Monte Carlo methods are a major approach in machine learning, statistical methods, and scientific computing. This project will also involve the training of graduate student researchers.<br/><br/><br/>This work involves mathematical studies of particle propagation in cluttered environments and Monte Carlo methods for Langevin equations. The first project concentrates on the effect of long-range correlations. This represents a novel direction in the theory of propagation in random media, as approximate models of propagation in slowly decorrelating media have not yet been developed. The goal is to explain how long-range correlations lead to time-scale separation of various phenomena. The second project concentrates on speeding up the convergence towards stationary measures, which is fundamental for the development of effective Markov Chain Monte Carlo algorithms. This is particularly relevant to Statistical Physics and understanding machine learning algorithms.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2406947","Two programs in the mathematical theory of fluids, gases, and plasmas","DMS","APPLIED MATHEMATICS","06/01/2024","05/14/2024","Dallas Albritton","WI","University of Wisconsin-Madison","Standard Grant","Pedro Embid","05/31/2027","$270,000.00","","dalbritton@wisc.edu","21 N PARK ST STE 6301","MADISON","WI","537151218","6082623822","MPS","126600","","$0.00","This is a project on the mathematical theory of fluids, gases, and plasmas, whose motion is modeled by nonlinear partial differential equations (PDEs). In many regimes of interest, fluids and plasmas exhibit extremely small scales; two key examples, which are relevant to this project, are the eddies which comprise a turbulent flow and the shock wave created by an aircraft as it breaks the sound barrier. This tendency toward small scales makes both theoretical and computational questions about fluids, plasmas, and the PDEs which model them highly challenging. In particular, traditional expectations about the predictive power of the standard PDEs can be violated in these regimes: In fluids, the most standard equations support significant non-uniqueness, while in gases and plasmas, they are not strictly valid inside a shock. This project will develop a mathematical theory to understand and overcome these challenges. This project will also provide opportunities for the integration of students into the research.<br/><br/>This project will carry out two programs in nonlinear partial differential equations (PDEs): (1) understanding non-uniqueness phenomena as an extreme form of instability in nonlinear PDEs, especially those arising in incompressible fluid mechanics, and (2) a rigorous PDE investigation of shock structure based on collisional kinetic theory. Regarding (1), the current non-uniqueness theory comes with caveats, e.g., the non-unique Navier-Stokes solutions are either forced or conjectural with supporting numerical evidence. The project will study problems of non-uniqueness and selection principle, without these caveats, in the Allen-Cahn and complex Ginzburg-Landau equations. Concerning (2), the project will investigate weak kinetic shock profiles for fundamental PDEs of plasma dynamics and advance the topological approach to constructing strong kinetic shock profiles.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2405161","Asymptotic Problems in Kinetic Theory","DMS","APPLIED MATHEMATICS","08/01/2024","05/14/2024","Lei Wu","PA","Lehigh University","Continuing Grant","Dmitry Golovaty","07/31/2027","$150,922.00","","lew218@lehigh.edu","526 BRODHEAD AVE","BETHLEHEM","PA","180153008","6107583021","MPS","126600","","$0.00","This project considers a set of problems in kinetic theory which deals with the motion of a vast number of particles, such as air or water flows, neutrons in the nuclear reactor, and even the collection of stars when modelling a galaxy. These immense systems can be analyzed on two scales: the microscopic scale, where first principles such as Newton's laws or the Schrödinger equation is employed to track the position and velocity of each individual particle, or the macroscopic scale, where statistical laws such as fluid mechanics and thermodynamics are utilized to predict the collective behavior of averaged properties like pressure and temperature. Kinetic theory serves as a bridge between these two approaches, utilizing probabilistic tools within the position-velocity space, also known as the phase space, to establish a mesoscopic description. The probability density of particles present in the phase space satisfies the Boltzmann-type or the Landau-type equations, which are evolutionary nonlinear partial differential equations. The broader impacts of the project consist of mentoring both graduate and undergraduate students, courses development, and running a summer school.<br/><br/>This project focuses on the asymptotic problems in kinetic equations, emphasizing the rigorous analysis to connect the aforementioned three scales of descriptions, and to quantitatively determine the scope of their applicability. The goal is to develop novel mathematical tools to characterize the multi-scale behaviors of these particle systems in applications such as medical imaging, gas dynamics, and nuclear fusion. Specifically, this project concentrates on the theory of hydrodynamic limits, a key step to tackle the so-called ""Hilbert's Sixth Problem"" to treat physics in an axiomatic manner. Novel techniques will be developed to study the asymptotic behavior of kinetic equations when the Knudsen number or Strouhal number, which measures the spatial or temporal scaling between particles collisions, shrinks to zero. The investigator will develop new nonlinear energy method, regularization, and remainder splitting techniques to tackle the non-classical boundary layer effects and the ?ghost? effects.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2404546","Free boundary and homogenization problems in active matter","DMS","APPLIED MATHEMATICS","09/01/2024","05/13/2024","Leonid Berlyand","PA","Pennsylvania State Univ University Park","Standard Grant","Pedro Embid","08/31/2027","$240,000.00","","lvb2@psu.edu","201 OLD MAIN","UNIVERSITY PARK","PA","168021503","8148651372","MPS","126600","054Z","$0.00","The project is aimed at the development and analysis of mathematical models of active matter (a.k.a. active materials), which is a rapidly growing research area. The key feature of active matter is the presence of ""active agents"" that convert energy from the environment into mechanical motion, e.g., a bacterium ""eats"" and converts chemical energy into mechanical motion. The research on active matter addresses the complex behavior of both biological systems and bio-inspired manufactured materials. Two areas of active matter will be studied: active gels and suspensions of active swimmers in fluids. In the first area, the focus will be on active gels such as the cytoskeleton gel that drives the motion of a living cell. Understanding this motion is important because of its role in wound healing, immune response, and cancer metastasis. The key challenge of the proposed mathematical models is the presence of a moving deformable boundary (""free boundary"") of the domain where the equations of motion of the active gel are defined. The project will address fundamental mathematical questions concerning the stability of solutions to differential equations in domains with a free boundary. In the second area, the focus will be on the collective motion of bacteria in anisotropic biofluids. The aim here is to provide a theoretical basis for understanding the behavior of complex biological systems such as dense bacterial colonies. The proposed work in both areas will result in the development of novel mathematical techniques that can be applied to various problems in biophysics and materials science. This award will provide opportunities for involvement of students in the research projects.<br/><br/>The proposed work is aimed at the rigorous analysis of recently developed free boundary and homogenization PDE models of active matter. The project will investigate two areas of active matter: (A) crawling cell motion on a substrate and (B) collective motion of microswimmers in anisotropic fluids. The goal of the proposed work is two-fold: to develop novel mathematical techniques for the analysis of active systems that are out of thermodynamic equilibrium, and to provide a better understanding of the biophysical phenomena in areas (A) and (B). In area (A), novel asymptotic techniques for spectral analysis of non-self-adjoint operators will be developed to rigorously prove bistability, i.e., the coexistence of two stable states of the cell: motile and sessile states. Due to the nonlinearity and non-self-adjointness of the free boundary problem that models cell motion, new techniques for both linear and nonlinear stability analysis will need to be developed. In area (B), the PI will develop novel stochastic homogenization techniques to obtain explicit asymptotic formulas for the effective rheological properties.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
+"2406626","Advances in Nonlinear Waves and Solitons in Integrable and Non-Integrable Systems","DMS","APPLIED MATHEMATICS","07/15/2024","05/15/2024","Barbara Prinari","NY","SUNY at Buffalo","Continuing Grant","Dmitry Golovaty","06/30/2027","$224,621.00","","bprinari@buffalo.edu","520 LEE ENTRANCE STE 211","AMHERST","NY","142282577","7166452634","MPS","126600","","$0.00","This project offers an in-depth investigation of the mathematical properties and physical applications of a special class of nonlinear waves. Over the past 50 years, a large body of knowledge has been accumulated on the nonlinear wave equations known as ?integrable systems?, which are used to model a wide variety of physically interesting phenomena, ranging from fluid dynamics and nonlinear optics, to low temperature physics and Bose-Einstein condensation (BEC). Several integrable systems are studied as part of the project: scalar and multicomponent nonlinear Schrodinger (NLS) type equations, Maxwell-Bloch equations describing the interaction of light with an active optical medium, discrete integrable and non-integral lattices such as the Ablowitz-Ladik equations, the discrete NLS, the Salerno model, etc. The project has concrete applications in nonlinear optics and BEC, and the investigator also collaborates with physicists to seek experimental validation of the results of obtained by the principal investigator (PI). It is therefore anticipated that the outcomes of the project will also provide practical information that will help scientists and engineers more broadly, thus potentially benefiting the society at large. As part of the project, the investigator is involved in the organization of several conferences and special sessions at larger professional meetings in the US and abroad, e.g., a 4 week-long program on ?Emergent Phenomena in Nonlinear Dispersive Waves?, to be held at Northumbria University, Newcastle, UK, in July-August 2024. Notably, the investigator organizes an event to showcase the research of female scientists. The training of graduate students is an integral component of the project, and two graduate students and a post-doctoral fellow are expected to work with the PI on research problems arising from this project.<br/> <br/>This project is aimed at advancing our theoretical and practical understanding of physically relevant integrable systems, as well as non-integrable systems in regimes that are not too far from the integrable ones, and it collects a suite of problems combined into a cohesive and coherent research effort, whose results will fundamentally further our knowledge of nonlinear waves and solitons, and their applications in various settings. Specifically, the investigator and her team pursue the following objectives: (i) formulation of a rigorous perturbation theory for dark and dark-bright solitons; (ii) development of a numerical inverse scattering transform on a nontrivial background; (iii) study of rogue waves, solitons and soliton interactions in scalar and coupled integrable and nonintegrable equations; (iv) investigation of the effect of radiation on the norming constants associated with the defocusing NLS equation, and their renormalization for solitonic models of condensates; (v) concrete applications to specific problems in BEC and nonlinear optics; (vi) study of Maxwell-Bloch systems both with rapidly decaying optical pulses and pulses with a constant background, and long-time asymptotics of their solutions. The project is carried out by developing and using a combination of: (a) exact methods, such as the inverse scattering transform, Backlund and Darboux transformations, and other direct methods; (b) asymptotic techniques, multiple scales and other perturbative tools; (c) state-of-the-art numerical simulations; (d) comparison with experiments in BEC and nonlinear optics.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2407592","Liquid crystals, their suspensions, and extreme wave phenomena in photonic devices","DMS","APPLIED MATHEMATICS","07/01/2024","05/13/2024","Raghavendra Venkatraman","UT","University of Utah","Standard Grant","Pedro Embid","06/30/2027","$230,111.00","","rv705@nyu.edu","201 PRESIDENTS CIR","SALT LAKE CITY","UT","841129049","8015816903","MPS","126600","054Z","$0.00","This project has two scientific research threads: a) liquid crystals (and their suspensions), and b) extreme wave phenomena in photonic devices. Concerning a): Certain materials, often made up of rod-like or disc-like molecules, display a range of ""liquid crystalline phases"" at suitable temperature/concentration ranges; these phases lie between the traditional (disordered) liquid and (ordered) crystalline phase, and thus possess varying degrees of order. Liquid crystals and their suspensions have revolutionized the industry of ultra-thin display devices and are showing promise in a number of other applications such as drug delivery, active matter and the orientation of carbon nanotubes. Concerning b): The photonic devices studied in this project include certain novel kinds of resonators, waveguides, and antennas. Particular focus is on devices made from epsilon near zero materials: these are materials whose dielectric permittivity is close to zero at the frequency of device operation. These novel devices find applications in efforts to enhance light-matter interactions. Common to both scientific threads of the proposed research is that their mathematical modeling leads to unconventional questions in partial differential equations and the calculus of variations that require new analytical tools that this project will develop. The scientific broader impact of this research is that its findings are expected to shed valuable insights on specific models used in application areas. These insights are expected to explain the results of direct numerical simulation (DNS) when this is possible, and more importantly, provide qualitative and (sometimes) quantitative information when DNS becomes formidable or even prohibitive. The project will also include a significant component on human resource development: a number of the projects in this award will be carried out in collaboration with graduate students and postdocs at the University of Utah. The trainees will learn, use, and develop tools in the calculus of variations, partial differential equations, geometric measure theory and homogenization theory.<br/><br/>Concerning liquid crystals, at the heart of their role in the aforementioned applications are both their anisotropic properties leading to their ordered phases on the one hand, and the rich phase transitions they can undergo between phases displaying varying degrees of order. This project will elucidate these effects through mathematical modeling and analysis and explain how they robustly result in a description of the shapes of the phase boundaries between the ordered nematic and disordered isotropic phase. A different goal of the research thread on liquid crystals is the justification of the widely used ""electrostatic"" description of the many-particle interactions in out-of-equilibrium liquid crystal colloids. Such a description is invaluable, because without it the modeling of liquid crystal colloids consists of a highly nonconvex, nonlinear problem in a domain exterior to the colloidal particles (coupled with other multi-physics aspects of the specific application). Concerning photonic devices: The mathematical problems addressed will involve either the Maxwell system (in 3D) or the scalar Helmholtz equation (in 2D) but with piecewise constant, complex coefficients; often such systems interact in interesting ways with geometric features such as corners, producing resonance effects. This project is aimed at understanding these effects, and some novel shape optimization problems arising from these physical situations.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2339212","Conference: Emergent Phenomena in Nonlinear Dispersive Waves","DMS","APPLIED MATHEMATICS","07/01/2024","01/23/2024","Mark Hoefer","CO","University of Colorado at Boulder","Standard Grant","Pedro Embid","06/30/2025","$15,000.00","Barbara Prinari","hoefer@colorado.edu","3100 MARINE ST","Boulder","CO","803090001","3034926221","MPS","126600","7556","$0.00","A one-month research-intensive satellite program by the Isaac Newton Institute, Cambridge, UK titled ""Emergent phenomena in nonlinear dispersive waves"" (PDW) will be held at Northumbria University and the University of Newcastle in Newcastle Upon Tyne, UK from July 22?August 16, 2024 (see the program website https://www.newton.ac.uk/event/pdw/). The concept of emergence will be explored in the context of dynamic and stochastic, multiscale dispersive wave phenomena described by nonlinear partial differential equations.  This program will host approximately 35 long-term, residential visitors at any given time and 60 or more participants in a one-week workshop. The diverse, international roster of participants includes leading researchers in the applied mathematical sciences. This National Science Foundation award provides travel support for early career applied mathematicians from the United States to participate in the workshop and the program. Traditionally underrepresented groups in applied mathematics will be encouraged to apply. This support enables sustained opportunities to interact with leading researchers from around the world. Such interactions and contacts are invaluable to beginning researchers, both to inspire research, and for professional development, thereby helping to cultivate the very best young researchers. These researchers will be the next generation of applied mathematicians who advance this and other applied mathematical fields of research.<br/><br/>Emergence is a powerful concept that plays a fundamental role in many areas of theoretical and mathematical physics. In a system composed of a very large number of elementary constituents, e.g. classical or quantum particles, the observable macroscopic behavior can be highly nontrivial. This transition from short-to-large scales is at the heart of hydrodynamic theories for inhomogeneous, dynamic many-body states. A very different kind of hydrodynamics arises when the microscopic constituents are waves. The subject of dispersive hydrodynamics?the theory of multiscale phenomena in nonlinear dispersive waves?has attracted much attention recently and was the focus of the 2022 ""Dispersive Hydrodynamics"" (HYD2) program held at the Isaac Newton Institute, Cambridge, UK. The satellite PDW program aims to capitalize on the successful HYD2 program to explore new frontiers of dispersive hydrodynamics in relation to the overarching theme of emergent phenomena in nonlinear waves. In particular, PDW will focus on three highly synergistic themes: (i) emergent hydrodynamics in integrable and nonintegrable systems; (ii) stability of nonlinear dispersive waves and emergent phenomena in unstable wave systems; (iii) soliton gas, generalized hydrodynamics and statistical mechanics of integrable systems.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2407511","CAREER: Singularities in fluids","DMS","APPLIED MATHEMATICS, ANALYSIS PROGRAM","04/15/2024","04/26/2024","Tristan Buckmaster","NY","New York University","Continuing Grant","Pedro Embid","08/31/2027","$187,507.00","","buckmaster@math.princeton.edu","70 WASHINGTON SQ S","NEW YORK","NY","100121019","2129982121","MPS","126600, 128100","1045","$0.00","Innumerable hydrodynamical phenomena are described in terms of singularities, of which perhaps the most well-known is the formation of shock waves resulting from a disturbance in a medium such as air or water moving faster than the local speed of sound. The goal of this project is to create a broad program for both research and pedagogical activities centered around the study of singularities in fluids. The award will provide research opportunities and training for postdoctoral scholars and will  leverage its research elements to design projects suitable for undergraduate students. The project will also aim at producing a foundational graduate textbook on shock waves in compressible fluids.<br/><br/>The research component is split into three projects: formation and development of shock waves, radial implosions from smooth initial data, and self-similar blow-up via neural networks. Building on previous work of the PI and his collaborators, the aim of the first project will be to provide the first full description of shock wave formation and development for the multi-dimensional compressible Euler equations. The second project involves further developing prior work on self-similar imploding solutions for isentropic compressible flows to investigate the possibility of new types of singularities. The third project involves utilizing physically informed neural networks to search for new forms of singularities in fluid, whose existence will be made rigorous through the aid of computer assisted proofs.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
diff --git a/Combinatorics/Awards-Combinatorics-2024.csv b/Combinatorics/Awards-Combinatorics-2024.csv
index aa6d35c..e74db43 100644
--- a/Combinatorics/Awards-Combinatorics-2024.csv
+++ b/Combinatorics/Awards-Combinatorics-2024.csv
@@ -1,5 +1,6 @@
 "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract"
 "2408960","Conference: A Celebration of Algebraic Combinatorics","DMS","Combinatorics","06/01/2024","05/14/2024","Lauren Williams","MA","Harvard University","Standard Grant","Stefaan De Winter","11/30/2025","$49,500.00","","williams@math.harvard.edu","1033 MASSACHUSETTS AVE STE 3","CAMBRIDGE","MA","021385366","6174955501","MPS","797000","7556","$0.00","The conference ``A celebration of algebraic combinatorics''  takes place on June 3-7, 2024, at the Harvard Geological lecture hall at Harvard University.  It covers many aspects of combinatorics, a field which was extensively developed by Richard Stanley through his work in algebraic, topological, geometric, and enumerative combinatorics.  The conference presents a chance to bring together both experts in the field and early career mathematicians to learn about the latest developments in the field.<br/><br/>The talks at the conference  cover a range of topics, ranging from total positivity, symmetric functions, Schubert calculus, poset topology, polytopes, to cluster algebras, log-concavity, the dimer model, and connections with probability.  Besides the talks, there are plans to have an open problem session. The website for the conference can be found at https://www.math.harvard.edu/event/math-conference-honoring-richard-p-stanley/<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
+"2408985","Conference: Mid-Atlantic Algebra, Geometry, and Combinatorics Workshop","DMS","Combinatorics","07/01/2024","05/15/2024","Nicola Tarasca","VA","Virginia Commonwealth University","Continuing Grant","Stefaan De Winter","06/30/2027","$11,368.00","Joel Lewis, Ying Anna Pun","tarascan@vcu.edu","910 WEST FRANKLIN ST","RICHMOND","VA","232849005","8048286772","MPS","797000","7556","$0.00","This award supports the next three editions of the Mid-Atlantic Algebra, Geometry, and Combinatorics (MAAGC) workshop, tentatively scheduled for October 12?13, 2024 at George Washington University, May 30?31, 2025 at CUNY Graduate Center, and May 29?30, 2026 at Virginia Commonwealth University. This conference series aims to bring together senior researchers and junior mathematicians in order to promote collaborations and regional interactions, while highlighting recent developments in algebraic combinatorics, algebraic geometry, representation theory, and other related fields. Each meeting will consist of four invited talks, a poster session for early-career participants, and a panel discussion on career advice, all while allowing for plenty of unstructured time for building mathematical connections.<br/><br/>The goals of MAAGC include helping researchers learn about cutting-edge developments and forge meaningful research collaborations and professional connections throughout the Mid-Atlantic region. The workshops are designed to strengthen and connect the scientific community in algebraic combinatorics and related areas, by facilitating positive interactions among undergraduate and graduate students, postdocs, and faculty at small colleges as well as research universities throughout the region. For more information, please visit the MAAGC website: http://maagc.info<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2411850","Conference: Dynamical and Statistical Combinatorics","DMS","Combinatorics","06/01/2024","05/13/2024","David Speyer","MI","Regents of the University of Michigan - Ann Arbor","Standard Grant","Stefaan De Winter","05/31/2025","$49,000.00","Gregg Musiker, Thomas Roby","speyer@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","797000","7556","$0.00","This award supports the upcoming conference ?Statistical and Dynamical Combinatorics,? taking place at MIT from June 26th to June 29th, 2024. Participants will include a broad and diverse spectrum of mathematicians including distinguished leaders, junior researchers and graduate students. Statistical and dynamical combinatorics has emerged as a topic of intensive research interest, studying different ways in which objects can be moved around and associated numbers that track different aspects of this movement.  Mathematical tools from both probability and combinatorics play a key role in analyzing these situations, and there is a strong need for the two communities to come together to work on them.  <br/><br/>Topics will include the following highly active areas: (1) Large scale randomness, (2) Markov processes, and (3) Dynamical algebraic combinatorics. All of these areas involve the use of statistics associated with combinatorial objects, each of which often admits multiple equivalent descriptions. Translating between the various forms in which these statistics and objects appear is one of the highlights of the subject. The conference website can be found at https://dept.math.lsa.umich.edu/~speyer/JIM/ .<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2349015","Combinatorics of Total Positivity: Amplituhedra and Braid Varieties","DMS","Combinatorics","09/01/2024","03/25/2024","Melissa Sherman-Bennett","MA","Massachusetts Institute of Technology","Standard Grant","Stefaan De Winter","08/31/2027","$180,000.00","","msherben@mit.edu","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","797000","","$0.00","The answers to real world problems, such as determining the behavior of particles in particle accelerators, are often quite complicated. Mathematics abstracts these complicated behaviors, and often reveals hidden structures; abstraction allows one to see the forest rather than the trees. For example, physicists Arkhani-Hamed and Trnka uncovered a high-dimensional mathematical object called the ""amplituhedron"" whose geometry should govern particle scattering. However, as abstraction increases, intuition decreases; it is easy to lose sight of the trees among the clouds. Algebraic combinatorics, as a mathematical discipline, is a tool to represent abstract mathematics in a more concrete way--similar to how a bar graph or scatter plot is a tool to represent a long list of numbers in a more intuitive way. In the case of the amplituhedron, combinatorics provides a way to break the amplituhedron up into smaller, simpler pieces. It also provides a way to visualize each piece, even though the pieces do not fit in three dimensions. It is through this combinatorics that the conjectural relationship between the amplituhedron and particle scattering is most apparent. In one project the PI will work to prove this conjectural relationship with collaborators Even-Zohar, Lakrec, Parisi, Tessler, and Williams. In general, the PI will seek to better understand the combinatorics of amplituhedra and related mathematical objects called cluster varieties. The PI will involve both undergraduate and graduate students in thisd research.<br/><br/>The broader mathematical context for the proposed projects is the theory of total positivity. Classically, a matrix is totally positive if all minors are positive. Lusztig extended the notion of total positivity to partial flag varieties, while Postnikov independently defined the positive Grassmannian. The combinatorics of total positivity is incredibly rich, leading to the definition of cluster algebras by Fomin and Zelevinsky. The PI proposes to study two generalizations of total positivity through a combinatorial lens. The first project concerns amplituhedra, which generalize the positive Grassmannian and arise in particle physics. The PI will work to resolve conjectures on the relationship between tilings of m=4 amplituhedra and the computation of scattering amplitudes, as well as various conjectures on tilings of m=2 amplituhedra. The second project concerns cluster structures on braid varieties, which generalize positive partial flag varieties. The PI will further develop the combinatorics of this cluster structure, investigating 3D plabic graphs and their relationship to weaves, and explore applications.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2344639","Conference: Conference on Enumerative and Algebraic Combinatorics","DMS","Combinatorics","02/15/2024","02/08/2024","Vincent Vatter","FL","University of Florida","Standard Grant","Stefaan De Winter","01/31/2025","$22,356.00","Miklos Bona, Zachary Hamaker, Andrew Vince","vatter@ufl.edu","1523 UNION RD RM 207","GAINESVILLE","FL","326111941","3523923516","MPS","797000","7556","$0.00","The Conference on Enumerative and Algebraic Combinatorics will take place at the University of Florida in Gainesville, Florida, February 25-27, 2024. The conference will feature 25 invited and contributed talks by leading researchers in the field as well as a poster session. By bringing together those working in both the Enumerative and Algebraic Combinatorics communities, attending researchers will have ample opportunity to learn about recent developments and develop new mathematics.<br/><br/>The aims of the conference are to present outstanding recent developments in both enumerative and algebraic combinatorics, with a particular focus on their overlap. Specific topics will include standard Young tableaux, permutations, partially ordered sets, symmetric functions, lattice paths, and compositions, all of which are amenable to both enumerative and algebraic study.  For more information see the conference web page: https://combinatorics.math.ufl.edu/conferences/sagan2024/<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
diff --git a/Geometric-Analysis/Awards-Geometric-Analysis-2024.csv b/Geometric-Analysis/Awards-Geometric-Analysis-2024.csv
index 8f9c8cd..2103349 100644
--- a/Geometric-Analysis/Awards-Geometric-Analysis-2024.csv
+++ b/Geometric-Analysis/Awards-Geometric-Analysis-2024.csv
@@ -1,5 +1,8 @@
 "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract"
+"2404599","Geometric Analysis and Complex Geometry","DMS","GEOMETRIC ANALYSIS","06/01/2024","05/15/2024","Valentino Tosatti","NY","New York University","Standard Grant","Qun Li","05/31/2027","$339,999.00","","tosatti@post.harvard.edu","70 WASHINGTON SQ S","NEW YORK","NY","100121019","2129982121","MPS","126500","","$0.00","The principal investigator's research is concerned with the study of geometric structures on a class of spaces known as complex manifolds, which are higher-dimensional curved spaces which can be defined using complex numbers. Complex manifolds are ubiquitous objects in mathematics, and have wide-ranging applications in physics and engineering. A notable class of complex manifolds is known as Calabi-Yau manifolds, which are a fundamental tool in theoretical high-energy physics, and one of the PI's main lines of research will enhance our understanding of these manifolds and their properties. Another major direction of research revolves around the study of an evolution equation for geometric spaces known as Ricci flow, which evolves a given shape in a continuous fashion aiming to make it as round as possible. In this process, singularities may develop, and understanding their nature is a central problem in the field. This project will investigate the nature of singularities that form as time goes to infinity, in the case when the geometric evolution exists for all positive time. For broader impacts, the PI will continue mentoring and advising graduate students and postdoctoral researchers, co-organize weekly seminars, organize conferences, workshops and summer schools, and disseminate their work at conferences, meetings, and seminars, as well as via scientific publications.<br/><br/>The PI will use techniques from geometric analysis, nonlinear partial differential equations and holomorphic dynamics to investigate fundamental questions about the geometry of complex manifolds and symplectic 4-manifolds. The first project aims to obtain a rather complete picture of the long-time behavior of immortal solutions of Ricci flow on compact Kahler manifolds. The main difficulty is that in the cases which are not already understood, the evolving metrics are volume-collapsed as time approaches infinity, and the expected limiting space is lower-dimensional. The second project is about understanding (1,1) cohomology classes on the boundary of the Kahler cone of a Calabi-Yau manifold, and the singularities of the closed positive currents that these classes contain. The third project will attack a conjecture of Donaldson program which aims to to extend Yau's solution of the Calabi Conjecture in Kahler geometry to symplectic 4-manifolds, and explore its applications in symplectic topology.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
+"2405270","Smooth Isotopy, Gauge Theory and Contact Geometry","DMS","GEOMETRIC ANALYSIS","07/01/2024","05/15/2024","Anubhav Mukherjee","NJ","Princeton University","Continuing Grant","Swatee Naik","06/30/2027","$67,222.00","","anubhavmaths@princeton.edu","1 NASSAU HALL","PRINCETON","NJ","085442001","6092583090","MPS","126500","","$0.00","One of the key areas of mathematics research involves understanding the shape of an object. In mathematical terms, exploring different types of mappings on and from the object aids in visualizing the space. Consequently, the space comprising all such mappings is pivotal in comprehending an object from a mathematical standpoint. The PI will delve into such a space, specifically focusing on the space of diffeomorphisms on a manifold, with a primary emphasis on dimension four. Historically, dimension four has been one of the most enigmatic dimensions, as various mathematical theories falter here. Therefore, the PI aims to develop new theories that can enhance our comprehension of this space. As a component of this initiative, the PI intends to establish connections and partnerships with various branches of mathematics. Moreover, the PI is actively engaged in mentoring at all levels. The projects offer a welcoming avenue for undergraduate and graduate students to engage in research.<br/><br/>One aspect of this project involves advancing theoretical frameworks for the smooth mapping class group of 4-manifolds, followed by utilizing diverse gauge theories to identify unconventional phenomena. The PI will pioneer new methodologies in this realm and endeavor to address longstanding conjectures concerning diffeomorphisms on 4-manifolds. Additionally, alongside investigating diffeomorphisms, the PI will explore the behavior of various embeddings of lower-dimensional manifolds within 4-manifolds. In the second phase, the PI will also allocate attention to three dimensions, seeking to discern relationships between different geometric structures. An illustrative example involves investigating the correlation between hyperbolic geometry and contact geometry.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2405393","Evolution Equations In Geometry","DMS","GEOMETRIC ANALYSIS","06/01/2024","05/13/2024","Tobias Colding","MA","Massachusetts Institute of Technology","Continuing Grant","Qun Li","05/31/2027","$129,353.00","","Colding@math.mit.edu","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","126500","","$0.00","Evolution equations are basic objects in the sciences, describing how natural phenomena change over time. For instance, modeling of a wide class of physical phenomena, such as crystal growth and flame propagation, leads to tracking fronts moving with curvature-dependent speed. Other natural evolutions leads to other equations, many of parabolic type, e.g. Ricci flow, and many have common features.  Broader impacts of the project are through mentoring graduate students and young researchers, organizing seminars, and the writing of textbooks and expository articles.<br/><br/>The bulk of this project concerns evolution equations. Mean curvature flow, as well as new methods for dealing with the diffeomorphism group for non compact spaces with applications to Ricci flow, will be major topics investigated. Other natural evolution equations coming from various branches of sciences will be studied as well as part of the project.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
+"2404845","Nonlinear PDE in Complex Geometry","DMS","GEOMETRIC ANALYSIS","07/01/2024","05/15/2024","Xi Sisi Shen","NY","Columbia University","Standard Grant","Qun Li","06/30/2027","$193,767.00","","xss@math.columbia.edu","615 W 131ST ST","NEW YORK","NY","100277922","2128546851","MPS","126500","","$0.00","The existence of canonical metrics has been an active research focus in geometry over the last century with immediate ties to the fields of general relativity and string theory. Canonical metrics can provide valuable insight into the specific geometry of geometric objects called manifolds. An example of canonical metrics are solutions to the Einstein field equations which relate the geometry of a spacetime, specifically the curvature, with the distribution of matter, energy and stress. In complex geometry, Calabi-Yau metrics, which are those with zero Ricci curvature, are a prime example of canonical metrics and their existence is directly related to solving a particular nonlinear partial differential equation called the complex Monge-Ampere equation. The equations of unified string theories are expected to yield new notions of canonical metrics as well as special geometries. This project aims to further our understanding of the existence of certain canonical metrics by developing necessary tools and new techniques in partial differential equations. Furthermore, the project will continue the PI's involvement in mentoring undergraduate and graduate students and organizing numerous seminars and conferences, with an emphasis on the inclusion of women and under-represented groups. <br/><br/>The project will pursue a program in which the PI will investigate several geometric problems related to canonical<br/>metrics on a complex manifold and the classification of algebraic varieties using the methods of nonlinear partial differential equations. One of the main goals is to prove existence of constant scalar curvature Hermitian metrics by obtaining a priori estimates and applying them to glean insight into the geometry of the complex manifold through the use of a continuity path or parabolic flow approach. In addition, the PI would like to transform our understanding of canonical metrics on a given manifold to the problem of searching for a family of canonical metrics given by the process of reducing a complex manifold to its minimal model, as per Mori's Minimal Model program, and the Analytic Minimal Model program by Song-Tian.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2404882","Homological Mirror Symmetry and Fukaya Categories from a Toric Perspective","DMS","GEOMETRIC ANALYSIS, EPSCoR Co-Funding","06/01/2024","05/14/2024","Andrew Hanlon","NH","Dartmouth College","Standard Grant","Eriko Hironaka","05/31/2027","$111,345.00","","andrew.d.hanlon@dartmouth.edu","7 LEBANON ST","HANOVER","NH","037552170","6036463007","MPS","126500, 915000","9150","$0.00","Interesting and impactful mathematics often arises when new connections are made between different fields of math. While even heuristic connections can be fruitful, mirror symmetry provides a fascinating direct connection, originating from modern physics, between algebraic geometry and symplectic topology that has led to major advances in both areas. Algebraic geometry is a rich and classical field of mathematics that explores shapes called algebraic varieties described by polynomial equations. Symplectic topology is a younger area that studies shapes built from a geometric formalism for classical mechanics by packaging solutions to certain partial differential equations into algebraic invariants. This project aims to deepen our understanding of the mirror symmetry phenomenon by building on new insights in a special case where the algebraic varieties are particularly symmetric. This will be done with the aim of verifying new cases of the homological mirror symmetry conjecture, exploring structural aspects of a symplectic invariant known as the Fukaya category, and investigating arithmetic aspects of mirror symmetry. The project will also involve undergraduate research projects on combinatorial problems coming from mirror symmetry.<br/><br/>The first technical goal of the project is to further develop functorial aspects of the toric homological mirror symmetry equivalence by enlarging the list of sheaves and functors that can be provably described in terms of Lagrangian submanifolds and geometric operations on them. These geometric functors will give a better understanding of homological mirror symmetry for singular varieties obtained by gluing toric varieties along toric strata, which can then be deformed to obtain new cases of the homological mirror symmetry conjecture. In the other direction, the project will seek to leverage the geometric flexibility of the Fukaya category to construct new group actions on derived categories of toric varieties. The project will also aim to determine when symplectic fibrations can be described in terms of cornered Liouville sectors resulting in a gluing formula for their Fukaya categories. Finally, the project will explore the extent to which the toric Frobenius morphism and its simple geometric description on the mirror can be extended to other classes of varieties with an eye towards generation time in the derived category.<br/><br/>This project is jointly funded by Topology and Geometric Analysis program and the Established Program to Stimulate Competitive Research (EPSCoR).<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2405175","Minimal Surfaces, Groups and Geometrization","DMS","GEOMETRIC ANALYSIS","11/01/2024","05/03/2024","Antoine Song","CA","California Institute of Technology","Continuing Grant","Qun Li","10/31/2027","$121,081.00","","aysong@caltech.edu","1200 E CALIFORNIA BLVD","PASADENA","CA","911250001","6263956219","MPS","126500","","$0.00","Differential geometry is a field which studies the shape of objects. Of particular importance are shapes that are ""optimal"" under natural constraints. An important class of optimal shapes is given by ""minimal surfaces"": a soap film spanning a metal wire, which tends to minimize its energy, is an example of minimal surface. This type of surfaces appears in many places in physics, but is also of intrinsic interest. The investigator will work on deforming smooth spaces, also called ""manifolds"", into an optimal shape by using the concept of minimal surfaces. Manifolds are ubiquitous in mathematics, and hopefully this approach will give new insights on their possible shapes. This project will moreover support student training and inclusion through seminars, workshops and knowledge dissemination efforts. <br/><br/><br/>The notion of ""geometric structure"" serves as a unifying concept in geometry and topology, as exemplified by the Uniformization theorem for surfaces and the Geometrization theorem for 3-manifolds. In those classical instances, geometric structures are essentially defined as homogenous spaces with a geometric discrete group action. In higher dimensions, those geometric structures are very rare, and perhaps too rigid compared to the diversity of closed manifolds. In this project, the investigator proposes to consider a more general and flexible notion: minimal surfaces in (possibly infinite dimensional) homogeneous spaces, invariant under a geometric discrete group action. With this point of view, the investigator will explore a series of questions which relates minimal surfaces to geometric group theory and representation theory. A typical problem is the following: what group can act geometrically on a connected minimal surface in a Hilbert sphere?<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2403557","Fundamental Gap Estimates and Geometry /Topology of Ricci Limit Spaces","DMS","GEOMETRIC ANALYSIS","07/01/2024","05/01/2024","Guofang Wei","CA","University of California-Santa Barbara","Continuing Grant","Qun Li","06/30/2027","$181,166.00","","wei@math.ucsb.edu","3227 CHEADLE HALL","SANTA BARBARA","CA","931060001","8058934188","MPS","126500","","$0.00","Various problems of mathematical physics can be modeled by the Laplacian or more general Schrodinger equations. The difference of the first two eigenvalues of the Laplacian is referred to as the fundamental gap, which represents the energy needed to excite a particle from ground level to the next level in quantum mechanics. The principal investigator will estimate the fundamental gap for various spaces. The proposed activities are related to optimal transport, information geometry and discrete geometry.  The project will also support educational activities and diversity through mentoring undergraduate and graduate students as well as postdocs; recruiting women and other underrepresented groups; organizing seminars, workshops and research programs promoting young scholars.<br/><br/>The project is centered around Riemannian geometry and geometric analysis with three parts. The first is about the fundamental gap estimates of the Laplacian with Dirichlet boundary conditions on a horoconvex domain in the hyperbolic space and convex domain in locally symmetric spaces by comparison with some suitable 1-dim model. The second concerns geometry and topology of spaces with Ricci curvature lower bound, especially the fundamental group of noncompact manifolds with nonnegative Ricci curvature; minimal volume entropy rigidity for metric measure spaces with curvature lower bounds.  The last is to study integral curvature for the critical power.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
diff --git a/Topology/Awards-Topology-2024.csv b/Topology/Awards-Topology-2024.csv
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--- a/Topology/Awards-Topology-2024.csv
+++ b/Topology/Awards-Topology-2024.csv
@@ -1,6 +1,8 @@
 "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract"
 "2405029","Collaborative Research: Algebraic K-theory and Equivariant Stable Homotopy Theory: Applications to Geometry and Arithmetic","DMS","TOPOLOGY","08/01/2024","05/14/2024","Andrew Blumberg","NY","Columbia University","Continuing Grant","Swatee Naik","07/31/2027","$21,883.00","","andrew.blumberg@columbia.edu","615 W 131ST ST","NEW YORK","NY","100277922","2128546851","MPS","126700","","$0.00","Algebraic topology began as the study of those algebraic invariants of geometric objects which are preserved under certain smooth deformations. Gradually, it was realized that the algebraic invariants called cohomology theories could themselves be represented by geometric objects, known as spectra. A central triumph of modern homotopy theory has been the construction of categories of ring spectra (representing objects for multiplicative cohomology theories) which are suitable for performing constructions directly analogous to those of classical algebra. This move has turned out to be incredibly fruitful, both by providing invariants which shed new light on old questions as well as by raising new questions which have unexpected connections to other areas of mathematics and physics. This research proposal studies such constructions in algebraic K-theory, the newly emerging field of Floer homotopy theory, and the foundations of equivariant stable homotopy theory. Broader impacts include workforce development in the form of graduate student advising, undergraduate and postdoc mentorship, high school mathematical science project mentorship, conference organization, and development of new education and training programs.<br/><br/>This proposal describes a broad research program to study a wide variety of problems in homotopy theory, geometry, and arithmetic. The PIs' prior work gives a complete description of the homotopy groups of algebraic K-theory of the sphere spectral at odd primes and a canonical identification of the fiber of the cyclotomic trace via a spectral lift of Tate-Poitou duality. In this proposal, the PIs describe a vast expansion of that argument to study the fiber of the cyclotomic trace on more general rings and schemes over algebraic p-integers in number fields and a related K-theory question more generally for other kinds of Artin duality. The prior work also leads to a new approach to the Kummer-Vandiver conjecture based on Bökstedt-Hsiang-Madsen's geometric Soule embedding that the PIs propose to study. The PIs' recent work with Yuan established a theory of topological cyclic homology (TC) relative to MU-algebras, where there are many interesting computations to explore. Prior work of PI Blumberg with Abouzaid building a Morava K-theory Floer homotopy type has opened new lines of research in Floer homotopy theory; this already has been used to resolve old conjectures in symplectic geometry. The PIs propose to extend this construction to its natural generality, building the homotopy type over MUP and KU and rigidifying the multiplication. They propose to obtain spectral models of deformed operations on quantum cohomology (i.e., quantum Steenrod operations). This work will have myriad applications in symplectic geometry and potentially have transformative impact on the Floer homotopy theory program. The PIs propose to resolve the longstanding confusion about the role of multiplicative norm maps in equivariant stable homotopy theory for positive dimensional compact Lie groups. This requires a new foundation for factorization homology and will lead to genuine equivariant factorization homology for positive dimensional compact Lie groups. In prior work, the PIs identified previously unknown multiplicative transfers on geometric fixed points of G-commutative ring spectra. The PIs propose to study how these fit into the foundations of G-symmetric monoidal categories; a first step is to establish new multiplicative splittings that have the feel of multiplicative versions of the tom Dieck splitting.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2415445","CAREER: Machine learning, Mapping Spaces, and Obstruction Theoretic Methods in Topological Data Analysis","DMS","TOPOLOGY, CDS&E-MSS","04/01/2024","04/02/2024","Jose Perea","MA","Northeastern University","Continuing Grant","Jodi Mead","04/30/2025","$336,550.00","","j.pereabenitez@northeastern.edu","360 HUNTINGTON AVE","BOSTON","MA","021155005","6173733004","MPS","126700, 806900","079Z, 1045","$0.00","Data analysis can be described as the dual process of extracting information from observations, and of understanding patterns in a principled manner. This process and the deployment of data-centric technologies have recently brought unprecedented advances in many scientific fields, as well as increased global prosperity with the advent of knowledge-based economies and systems. At a high level, this revolution is driven by two thrusts: the modern technologies which allow for the collection of complex data sets, and the theories and algorithms we use to make sense of them. That said, and for all its benefits, extracting actionable knowledge from data is difficult. Observations gathered in uncontrolled environments are often high-dimensional, complex and noisy; and even when controlled experiments are used, the intricate systems that underlie them --- like those from meteorology, chemistry, medicine and biology --- can yield data sets with highly nontrivial underlying topology. This refers to properties such as the number of disconnected pieces (i.e., clusters), the existence of holes or the orientability of the data space. The research funded through this CAREER award will leverage ideas from algebraic topology to address data science questions like visualization and representation of complex data sets, as well as the challenges posed by nontrivial topology when designing learning systems for prediction and classification. This work will be integrated into the educational program of the PI through the creation of an online TDA (Topological Data Analysis) academy, with the dual purpose of lowering the barrier of entry into the field for data scientists and academics, as well as increasing the representation of underserved communities in the field of computational mathematics. The project provides research training opportunities for graduate students.<br/><br/>Understanding the set of maps between topological spaces has led to rich and sophisticated mathematics, for it subsumes algebraic invariants like homotopy groups and generalized (co)homology theories. And while several data science questions are discrete versions of mapping space problems --- including nonlinear dimensionality reduction and supervised learning --- the corresponding theoretical and algorithm treatment is currently lacking. This CAREER award will contribute towards remedying this situation. The research program articulated here seeks to launch a novel research program addressing the theory and algorithms of how the underlying topology of a data set can be leveraged for data modeling (e.g., in dimensionality reduction) as well as when learning maps between complex data spaces (e.g., in supervised learning). This work will yield methodologies for the computation of topology-aware and robust multiscale coordinatizations for data via classifying spaces, a computational theory of topological obstructions to the robust extension of maps between data sets, as well as the introduction of modern deep learning paradigms in order to learn maps between non-Euclidean data sets.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
+"2409099","Conference: 2024-2026 Graduate Student Conference in Geometry, Topology, and Algebra","DMS","ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","05/15/2024","05/15/2024","Matthew Stover","PA","Temple University","Standard Grant","Swatee Naik","04/30/2027","$90,000.00","David Futer, Jaclyn Lang","mstover@temple.edu","1805 N BROAD ST","PHILADELPHIA","PA","191226104","2157077547","MPS","126400, 126700","7556","$0.00","This award supports the next three events in the Annual Graduate Student Conference series in Algebra, Geometry, and Topology (GTA Philadelphia). The next conference will be held on May 31-June 2, 2024 at Temple University. The conference will bring together over 80 graduate students at all levels and from a variety of backgrounds and universities, along with four distinguished plenary speakers that work at the interface of algebra, geometry, and topology. Supplementing lectures by faculty and students, the conference features a professional development panel focused on career building and social responsibility. The conference provides a rare opportunity for a large number of early career mathematicians with similar research interests to come together and develop mathematical relationships. In addition, it strongly supports interactions between graduate students from different schools, different backgrounds, and different research areas.<br/><br/>The large majority of lectures will be given by graduate students, supplying them with opportunities to practice presenting their research ideas and interests to fellow students. The conference strives to include a wide range of topics and a broad diversity of speakers. In addition, talks by distinguished plenary speakers will provide insights into how different parts of algebra, geometry, and topology are connected, open research questions of interest, and recent techniques used in groundbreaking work in these fields. For further information, see https://math.temple.edu/events/conferences/gscagt/.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
+"2405301","The Topology of 3- and 4-Manifolds","DMS","OFFICE OF MULTIDISCIPLINARY AC, TOPOLOGY","07/01/2024","05/15/2024","Alexander Zupan","NE","University of Nebraska-Lincoln","Standard Grant","Swatee Naik","06/30/2027","$317,407.00","","zupan@unl.edu","2200 VINE ST","LINCOLN","NE","685032427","4024723171","MPS","125300, 126700","9150","$0.00","The field of topology involves understanding properties of abstract shapes that are unchanged by twisting, stretching, and bending (but not breaking or tearing).  A n-dimensional manifold is a space that locally resembles n-dimensional real space.  For example, the surface of a donut is a two-dimensional manifold, because under very high magnification, this surface looks like a two-dimensional plane.  Three-dimensional objects arise naturally in our physical world, and four-dimensional objects can be motivated by thinking about the evolution of three-dimensional objects over time.  Notably, low-dimensional topology has a number of interesting applications to biology, chemistry, physics, and quantum computing.  This project focuses on the search for deep connections between manifold theory in dimensions three and four.  In addition, the project includes funding for graduate and undergraduate student research, and it will support the Great Plains Alliance, a program that pairs graduate students with speaking opportunities at other institutions for the purpose of broadening the impact of their work and promoting graduate school in mathematics to the undergraduate attendees.  The project will also fund the Distinguished Women in Mathematics colloquium series at the University of Nebraska-Lincoln, the PI?s home institution.  This series connects UNL faculty and graduate students with prominent women mathematicians and their research.<br/><br/>Topology in dimension three has seen an explosion of activity over the last several decades, and a number of important open problems have now been resolved.  In contrast, the topology of four-dimensional manifolds has become an increasingly active area of research, motivated by fundamental conjectures that have stubbornly resisted progress.  Two of the most famous examples include the smooth four-dimensional Poincaré conjecture (SPC4) and the slice-ribbon conjecture.  Recently, the PI has shown that a substantial family of four-manifolds satisfies the SPC4 in joint work with Jeffrey Meier.  The work connects four-dimensional handle calculus with results about Dehn surgery on knots and links in three-manifolds; it brings together a wide range of tools and techniques; and it subsumes several historically important results.  The collection of manifolds can be characterized by families of links, including some of the most promising potential counterexamples to the slice-ribbon conjecture.  This project describes a varied set of problems stemming from past work and interweaving ideas from knot theory, three-manifolds, and smooth four-manifold topology.  Specific objectives include proving additional cases of the SPC4, finding new relationships between the topology of certain homotopy four-spheres and the Andrews-Curtis conjecture in combinatorial group theory, developing connections between three- and four-dimensional knot invariants, and utilizing bridge trisections in new constructions of surfaces in four-manifolds.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2405030","Collaborative Research: Algebraic K-theory and Equivariant Stable Homotopy Theory: Applications to Geometry and Arithmetic","DMS","TOPOLOGY","08/01/2024","05/14/2024","Michael Mandell","IN","Indiana University","Continuing Grant","Swatee Naik","07/31/2027","$69,737.00","","mmandell@indiana.edu","107 S INDIANA AVE","BLOOMINGTON","IN","474057000","3172783473","MPS","126700","","$0.00","Algebraic topology began as the study of those algebraic invariants of geometric objects which are preserved under certain smooth deformations. Gradually, it was realized that the algebraic invariants called cohomology theories could themselves be represented by geometric objects, known as spectra. A central triumph of modern homotopy theory has been the construction of categories of ring spectra (representing objects for multiplicative cohomology theories) which are suitable for performing constructions directly analogous to those of classical algebra. This move has turned out to be incredibly fruitful, both by providing invariants which shed new light on old questions as well as by raising new questions which have unexpected connections to other areas of mathematics and physics. This research proposal studies such constructions in algebraic K-theory, the newly emerging field of Floer homotopy theory, and the foundations of equivariant stable homotopy theory. Broader impacts include workforce development in the form of graduate student advising, undergraduate and postdoc mentorship, high school mathematical science project mentorship, conference organization, and development of new education and training programs.<br/><br/>This proposal describes a broad research program to study a wide variety of problems in homotopy theory, geometry, and arithmetic. The PIs' prior work gives a complete description of the homotopy groups of algebraic K-theory of the sphere spectral at odd primes and a canonical identification of the fiber of the cyclotomic trace via a spectral lift of Tate-Poitou duality. In this proposal, the PIs describe a vast expansion of that argument to study the fiber of the cyclotomic trace on more general rings and schemes over algebraic p-integers in number fields and a related K-theory question more generally for other kinds of Artin duality. The prior work also leads to a new approach to the Kummer-Vandiver conjecture based on Bökstedt-Hsiang-Madsen's geometric Soule embedding that the PIs propose to study. The PIs' recent work with Yuan established a theory of topological cyclic homology (TC) relative to MU-algebras, where there are many interesting computations to explore. Prior work of PI Blumberg with Abouzaid building a Morava K-theory Floer homotopy type has opened new lines of research in Floer homotopy theory; this already has been used to resolve old conjectures in symplectic geometry. The PIs propose to extend this construction to its natural generality, building the homotopy type over MUP and KU and rigidifying the multiplication. They propose to obtain spectral models of deformed operations on quantum cohomology (i.e., quantum Steenrod operations). This work will have myriad applications in symplectic geometry and potentially have transformative impact on the Floer homotopy theory program. The PIs propose to resolve the longstanding confusion about the role of multiplicative norm maps in equivariant stable homotopy theory for positive dimensional compact Lie groups. This requires a new foundation for factorization homology and will lead to genuine equivariant factorization homology for positive dimensional compact Lie groups. In prior work, the PIs identified previously unknown multiplicative transfers on geometric fixed points of G-commutative ring spectra. The PIs propose to study how these fit into the foundations of G-symmetric monoidal categories; a first step is to establish new multiplicative splittings that have the feel of multiplicative versions of the tom Dieck splitting.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2404953","Heegaard Diagrams and Holomorphic Disks","DMS","TOPOLOGY","07/01/2024","05/13/2024","Peter Ozsvath","NJ","Princeton University","Standard Grant","Swatee Naik","06/30/2027","$370,000.00","","petero@math.princeton.edu","1 NASSAU HALL","PRINCETON","NJ","085442001","6092583090","MPS","126700","","$0.00","Heegaard Floer homology is a tool for studying the topology of three- and four-dimensional objects, discovered by the PI in collaboration with Zoltan Szabo. The construction is deeply rooted in the interaction between modern mathematical methods and ideas from mathematical physics; and indeed, Heegaard Floer homology has found interactions with many other mathematical fields, including symplectic geometry, analysis, representation theory, and homological algebra. But in its essence, Heegaard Floer homology was designed to study low-dimensional phenomena, such as how knotted a circle can be in a three-dimensional manifold, how knotted two-dimensional surfaces can be in four-dimensional space, and how interesting a four-dimensional space can be.  The project aims to further explore the topological applications of Heegaard Floer homology; and to further build the foundations of this invariant, both to develop computational schemes and to build a broader theoretical framework into which the theory fits in algebraically. The project will also help support graduate students studying in low-dimensional topology and related areas.<br/><br/>The project will further develop bordered aspects of Heegaard Floer homology, specifically for dealing with its U-unspecialized versions, which are more sensitive to four-dimensional differential topology than the U-specialized versions. Parts of the project involve collaborations with other researchers, including Robert Lipshitz, Zoltan Szabo, and Dylan Thurston. Joint work with Lipshitz and Thurston sets up the algebraic background needed for this extension of weighted A-infinity algebras, their tensor products, and modules; constructed the weighted A-infinity module for the torus; weighted modules associated to three-manifolds with (bordered) torus boundary. The project aims at proving a pairing theorem, which expresses the Heegaard Floer homology module of a union of two three-manifolds glued along a torus as a suitable tensor product of the modules associated to the two manifolds. The project also aims to generalize the picture to three-manifolds whose boundary is a closed, hyperbolic surface. In a different direction, the project aims to give a description of the full (unspecialized) knot Floer complex in terms of a knot projection, as a tensor product of bimodules associated to the elementary pieces.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."
 "2403558","Spectrification of Homology Theories in Low Dimensional Topology","DMS","TOPOLOGY","09/01/2024","05/02/2024","Sucharit Sarkar","CA","University of California-Los Angeles","Continuing Grant","Swatee Naik","08/31/2027","$65,040.00","","sucharit@math.ucla.edu","10889 WILSHIRE BLVD STE 700","LOS ANGELES","CA","900244200","3107940102","MPS","126700","","$0.00","Topology is the branch of mathematics that studies shapes of spaces. Knot theory is an important sub-field of topology where one studies one-dimensional objects inside three-dimensional spaces, for example, knotted pieces of strings inside the three-dimensional space that we live in. Knot theory is useful for a variety of applications, such as for studying DNA knotting, analyzing orbits in magnetic fields, or creating new data encryption schemes. One of the fundamental problems in knot theory is to study if a knot can be transformed into another without tearing or crossing itself; knot invariants are mathematical objects (such as numbers or groups) which one associates to knots which remain unchanged during such a transformation, and are therefore, widely used in knot theory. Occasionally, one imposes additional restrictions on the knots---if one imagines a knot to be a path traced out by a particle moving in the three-dimensional space, then these restrict the velocity of the particle depending on its position. Knots with such restrictions are called Legendrian knots, and these have many real-world applications as well, such as motion planning for robotics. The current topology project will focus on knot theory, and will create new knot and Legendrian knot invariants based on existing ones. Broader impacts of the project are through workshop organization, graduate student mentoring, undergraduate research, high school outreach, and the writing of a textbook for Directed Reading Programs.<br/><br/>This project will concentrate on three families of modern knot and Legendrian knot invariants: Khovanov homology, knot Floer homology, and Legendrian contact homology. These invariants are all of the homological type, that is, they take the form of chain complexes whose chain homotopy types are (Legendrian) knot invariants. The project will construct and study spectrifications of these theories, which are cellular spaces whose cellular chain complex is the original chain complex, and whose stable homotopy type is also a (Legendrian) knot invariant. For the three families of invariants, three specific goals of the project are: to study the behavior of the odd Khovanov spectrum invariant under disjoint union, to prove that the knot Floer spectrum is a knot invariant, and to construct new Legendrian contact spectrum generalizing Legendrian contact homology.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."